Free NCERT Solutions, Notes & MCQs for Class 9–12

QUADRATIC EQUATIONS - MCQs

🎯 Knowledge Check

Maths — QUADRATIC EQUATIONS

50 Questions Class 10 MCQs

Which represents the standard form of a quadratic equation?

a a. \(x^3+2x^2+3x+1=0\) b b. \(2x^2-5x+7=0\) c c. \(x+3=0\) d d. \(x^4-x=0\)

The discriminant of \(x^2-4x+4=0\) is:

a a. 0 b b. 16 c c. -16 d d. 32

\(D>0\) means roots are:

a a. Real and equal b b. Real and distinct c c. No real roots d d. Imaginary

Sum of roots for \(ax^2+bx+c=0\) is:

a a. \(c/a\) b b. \(-b/a\) c c. \(b/a\) d d. \(-c/a\)

Product of roots for \(ax^2+bx+c=0\) is:

a a. \(-b/a\) b b. \(c/a\) c c. \(b/a\) d d. \(-c/a\)

Roots of \(x^2-5x+6=0\):

a a. 2, 3 b b. 1, 6 c c. -2, -3 d d. 5, 1

\(2x^2+3x+1=0\) has how many real roots?

a a. 0 b b. 1 c c. 2 equal d d. 2 distinct

Equation with roots 2, -3:

a a. \(x^2+x-6=0\) b b. \(x^2-x+6=0\) c c. \(x^2-x-6=0\) d d. \(x^2+x+6=0\)

\(D=0\) implies:

a a. Distinct real roots b b. Equal real roots c c. No real roots d d. Positive roots

Nature of roots for \(3x^2-6x+3=0\):

a a. Distinct real b b. Equal real c c. No real d d. Two positive

Which is quadratic?

a a. \(x^3=0\) b b. \(x^2=4\) c c. \(x+1=0\) d d. \(x^4=1\)

Product of roots \(4x^2+4x+1=0\):

a a. \(1/4\) b b. \(-1/4\) c c. 1 d d. 4

Sum of roots \(x^2-7x+10=0\):

a a. 7 b b. -7 c c. 10 d d. -10

Which has \(D<0\)?

a a. \(x^2+1=0\) b b. \(x^2-1=0\) c c. \(x^2=0\) d d. \(x^2-2x+1=0\)

Roots of \(x^2+2x-3=0\):

a a. 1, -3 b b. -1, 3 c c. 2, -1.5 d d. -2, 1.5

Quadratic formula is:

a a. \(\frac{-b\pm\sqrt{D}}{2a}\) b b. \(\frac{b\pm\sqrt{D}}{2a}\) c c. \(\frac{-b\pm D}{2a}\) d d. \(\frac{b\pm D}{a}\)

For \(x^2-4=0\), roots:

a a. 2, -2 b b. 4, 0 c c. -4, 4 d d. 2, 2

If roots are equal, then:

a a. \(D>0\) b b. \(D=0\) c c. \(D<0\) d d. \(a=0\)

\(5x^2+5=0\) has:

a a. Two real roots b b. One real root c c. No real roots d d. Infinite roots

Sum for roots \(1/2,3/2\):

a a. 1 b b. 2 c c. \(3/4\) d d. \(9/4\)

Solve \(x^2-7x+12=0\):

a a. 3, 4 b b. -3, -4 c c. 7, 12 d d. 1, 12

Using formula, \(2x^2-3x-2=0\):

a a. 2, \(-1/2\) b b. -2, \(1/2\) c c. \(3/2\), \(-2/3\) d d. 1, -2

Verify if \(x=2\) satisfies \(x^2-4x+4=0\):

a a. Yes b b. No c c. Partially d d. Cannot say

Roots \(x^2+5x+6=0\):

a a. -2, -3 b b. 2, 3 c c. -5, -6 d d. 1, 6

\(D\) of \(3x^2+6x+3=0\):

a a. 0 b b. 9 c c. -9 d d. 36

Solve \(x^2+x-12=0\):

a a. 3, -4 b b. -3, 4 c c. 12, -1 d d. 1, 12

Product for \(4x^2-8x+3=0\):

a a. \(3/4\) b b. \(-3/4\) c c. \(8/4\) d d. 3

Nature \(x^2+2x+2=0\):

a a. Real distinct b b. Real equal c c. No real d d. Positive

Equation roots 1, 1:

a a. \(x^2-2x+1=0\) b b. \(x^2+2x+1=0\) c c. \(x^2-x+1=0\) d d. \(x^2+x+1=0\)

Solve \(6x^2-7x-3=0\):

a a. \(3/2\), \(-1/2\) b b. \(-3/2\), \(1/2\) c c. \(7/6\), 3 d d. 1, -3

\(x^2-2x-8=0\) roots:

a a. 4, -2 b b. -4, 2 c c. 8, 0 d d. 2, -4

If one root 3, sum 7: other root?

a a. 4 b b. -4 c c. 21 d d. 3

Completing square \(x^2+6x+8=0\):

a a. -4, -2 b b. 4, 2 c c. -3, -3 d d. 3, 3

\(9x^2-6x+1=0\) roots:

a a. Equal b b. Distinct c c. Imaginary d d. Zero

Product roots zero implies:

a a. \(c=0\) b b. \(b=0\) c c. \(a=0\) d d. \(D=0\)

Solve \(x^2-9=0\):

a a. 3, -3 b b. 9, 0 c c. -9, 9 d d. 3, 3

\(D\) for \(x^2+4x+4=0\):

a a. 0 b b. 16 c c. -16 d d. 32

Roots \(2x^2+5x+3=0\):

a a. -1, \(-3/2\) b b. 1, \(3/2\) c c. \(-5/2\), -3 d d. 2, \(3/5\)

If \(D=16\), \(a=1\), \(b=-8\): \(c=\)?

a a. 12 b b. -12 c c. 8 d d. 16

Verify \(x=-3\) for \(x^2+2x-3=0\):

a a. Yes b b. No c c. Zero d d. Positive

Rectangle length=width+2, area 15: equation?

a a. \(x^2+2x-15=0\) b b. \(x^2-2x+15=0\) c c. \(x^2+2x+15=0\) d d. \(2x^2-15=0\)

Speed \(x\) km/h, return \(x+5\), time diff 1h for 120km:

a a. \(x^2+5x-600=0\) b b. \(x^2-5x-600=0\) c c. \(x^2+10x-600=0\) d d. \(x^2-10x+600=0\)

Two numbers sum 10, product 21: equation?

a a. \(x^2-10x+21=0\) b b. \(x^2+10x-21=0\) c c. \(x^2-21x+10=0\) d d. \(10x^2+21=0\)

Father 3×son age, 15yrs ago 5×: son now?

a a. 18 b b. 15 c c. 20 d d. 21

Boat speed \(x\) upstream, downstream \(x+10\), diff 24km in 4h:

a a. \(x^2+10x-60=0\) b b. \(x^2-10x-60=0\) c c. \(2x^2-240=0\) d d. \(x^2+20x-60=0\)

Garden length=width+4, area=96: equation?

a a. \(x^2+4x-96=0\) b b. \(x^2-4x-96=0\) c c. \(x^2+8x+96=0\) d d. \(x(x+4)=96\)

Projectile \(h=10t-5t^2\) max at?

a a. \(t=1\) b b. \(t=2\) c c. \(t=5\) d d. \(t=10\)

Numbers differ by 3, sum squares 61: larger?

a a. 7 b b. 5 c c. 8 d d. 4

Trains \(x,x+2\) km/h, relative 80km/h covers 240km:

a a. \(x^2+2x-1600=0\) b b. \(x(x+2)=240\) c c. \(2x^2=240\) d d. \(x^2-2x-240=0\)

Roots \(\alpha,\beta\): \(\alpha+\beta=5\), \(\alpha\beta=6\), then \(\alpha^2+\beta^2=\)?

a a. 13 b b. 25 c c. 30 d d. 11

📚

ACADEMIA AETERNUM तमसो मा ज्योतिर्गमय · Est. 2025

Sharing this chapter

Mathematics | Maths Class 10

Mathematics | Maths Class 10 — Complete Notes & Solutions · academia-aeternum.com

🎓 Class 10 📐 Maths 📖 NCERT ✅ Free Access 🏆 CBSE · JEE

Share on

X / Twitter

Facebook

academia-aeternum.com/blogs/MCQs/mathematics/X-Class/quadratic-equations-x-mcqs/ Copy link

💡

Exam tip: Sharing chapter notes with your study group creates a reinforcement loop. Teaching a concept is the fastest path to mastering it.

Frequently Asked Questions

A quadratic equation is an equation of the form \(ax^2 + bx + c = 0\) where \(a,\ b\, c\) are real numbers and \(a \neq 0\).

If \(a = 0\), the equation becomes linear and no longer contains a squared term, so it cannot be quadratic.

The standard form is \(ax^2 + bx + c = 0\).

The word “quadratic” comes from “quad,” meaning square, because the highest power of the variable is 2.

The solutions of \(ax^2 + bx + c = 0\) are \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\).

The discriminant \(D\) is the expression \(b^2 - 4ac\) found inside the square root of the quadratic formula.

It indicates two distinct real roots.

It indicates one real and repeated root.

It indicates no real roots; the solutions are complex.

By splitting the middle term into two terms whose product is (ac), factoring the expression, and using the zero-product property.

If \(pq = 0\), then either \(p = 0\) or \(q = 0\). It is used to solve factored quadratic equations.

It means expressing \(bx\) as the sum of two terms whose product equals \(ac\), helping in factorization.

It is a method of rewriting a quadratic as a perfect square expression to solve the equation.

It helps derive the quadratic formula and solve equations that are not easy to factor.

Ensure \(a = 1\), take half of the coefficient of \(x\), square it, add it to both sides, form a perfect square, and solve.

QUADRATIC EQUATIONS - MCQs

Maths — QUADRATIC EQUATIONS

Frequently Asked Questions

Recent Posts

QUADRATIC EQUATIONS – Learning Resources

Detailed Notes

True / False

NCERT Solutions

Let's Connect

QUADRATIC EQUATIONS - MCQs

Maths — QUADRATIC EQUATIONS

Frequently Asked Questions

Q 01 What is a quadratic equation?

Q 02 Why must the coefficient of \(x^2\) be non-zero?

Q 03 What is the standard form of a quadratic equation?

Q 04 What is the meaning of the term “quadratic”?

Q 05 What is the quadratic formula?

Q 06 What is the discriminant?

Q 07 What does \(D > 0\) indicate?

Q 08 What does \(D = 0\) indicate?

Q 09 What does \(D < 0\) indicate?

Q 10 How do you solve a quadratic equation by factorization?

Q 11 What is the zero-product property?

Q 12 What does “splitting the middle term” mean?

Q 13 What is the method of completing the square?

Q 14 Why is completing the square important?

Q 15 What are the steps of completing the square?

Recent Posts

QUADRATIC EQUATIONS – Learning Resources

Detailed Notes

True / False

NCERT Solutions

Let's Connect