NCERT Class 10 Maths — Chapter 4

Exercise 4.3: Completing the Square and Quadratic Formula

Learn two powerful methods: completing the square and the quadratic formula. The formula works for every quadratic, even when factorisation fails.

completing the squarequadratic formuladiscriminant

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Extra Practice Questions

These questions cover the same concepts as Exercise 4.3. Try solving them to build confidence before or after the textbook exercise.

A plane covers a distance of 1200 km at a certain speed. If its speed is increased by 100 km/hr, the journey takes 1 hour less. Find the original speed of the plane.

A.300 km/hr

B.400 km/hr

C.200 km/hr

D.250 km/hr

Which of the following equations is NOT a quadratic equation?

A.(x - 2)² + 1 = 2x - 3

B.x(x + 1) + 8 = (x + 2)(x - 2)

C.x(2x + 3) = x² + 1

D.(x + 2)³ = x³ - 4

The product of two consecutive positive integers is 306. Which of the following quadratic equations represents this situation?

A.x² + x + 306 = 0

B.x² - x + 306 = 0

C.x² + x - 306 = 0

D.x² - x - 306 = 0

Find the value of 'k' for which the quadratic equation (k - 12)x² + 2(k - 12)x + 2 = 0 has equal roots.

A.k = 12

B.k = 10

C.k = 8

D.k = 14

Solve for x: 1/(x+4) - 1/(x-7) = 11/30, where x ≠ -4, 7.

A.x = 1, x = 2

B.x = -1, x = -2

C.x = 1, x = -2

D.x = -1, x = 2

If the discriminant of a quadratic equation ax² + bx + c = 0 is D, then the equation has no real roots if D is _____

A.D > 0

B.D = 0

C.D < 0

D.D ≥ 0

If the roots of a quadratic equation are 2 and -3/2, what is the quadratic equation?

A.2x² - x - 6 = 0

B.2x² + x - 6 = 0

C.2x² - 7x + 6 = 0

D.3x² + x - 2 = 0

Which of the following statements is true about the quadratic equation x² + 2x + 5 = 0?

A.It has two distinct real roots.

B.It has two equal real roots.

C.It has no real roots.

D.It has one real root and one imaginary root.

A student tried to solve the quadratic equation x² - 6x + 8 = 0 by completing the square. His steps were: 1. x² - 6x = -8 2. x² - 6x + (6/2)² = -8 + (6/2)² 3. (x - 3)² = -8 + 9 4. (x - 3)² = 1 5. x - 3 = 1 6. x = 4 Which of the following describes the mistake made by the student?

A.Mistake in step 1: Did not move the constant term correctly.

B.Mistake in step 2: Added an incorrect term to complete the square.

C.Mistake in step 3: Incorrectly factored the perfect square trinomial.

D.Mistake in step 5: Did not consider both positive and negative square roots.

If x = 2/3 is a root of the quadratic equation 3x² + kx - 2 = 0, find the value of k.

A.k = 1

B.k = 2

C.k = -1

D.k = -2

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