NCERT Class 10 Maths — Chapter 4

Exercise 4.1: Check if an Equation is Quadratic

Convert equations to standard form ax² + bx + c = 0 and check if they're actually quadratic.

standard formidentifying quadratic equations

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Extra Practice Questions

These questions cover the same concepts as Exercise 4.1. Try solving them to build confidence before or after the textbook exercise.

When solving a quadratic equation, which of the following scenarios would make the quadratic formula (x = [-b ± √(b² - 4ac)] / 2a) the *most suitable* method compared to factorization?

A.When the equation has simple integer roots like 2 and 3.

B.When the coefficients 'a', 'b', and 'c' are very large numbers.

C.When the discriminant (b² - 4ac) is a perfect square.

D.When the roots are irrational numbers or not easily found by factorization.

For what values of 'm' does the quadratic equation x² - 2(m+1)x + (m²+4m+1) = 0 have real and distinct roots?

A.m < 0

B.m > 0

C.m = 0

D.m < -1

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

The equation (x² + x)² + 4(x² + x) - 12 = 0 can be solved by making a suitable substitution. Which of the following represents the correct set of solutions for x?

A.x = 1, -2, -3, 2

B.x = 1, -2

C.x = -3, 2

D.x = 1, 2, 3, -2

Solve for x: (x / (x+1)) + ((x+1) / x) = 34/15, where x ≠ 0, x ≠ -1.

A.x = 1/2 or x = -2/3

B.x = 3/2 or x = -5/2

C.x = -1/2 or x = 2/3

D.x = -3/2 or x = 5/2

A takes 6 days less than B to finish a piece of work. If both A and B together can finish the work in 4 days, find the number of days B alone would take to finish the work.

A.6 days

B.8 days

C.10 days

D.12 days

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

If α and β are the roots of the quadratic equation 3x² - 4x + 1 = 0, find the value of (1/α) + (1/β).

A.1/4

B.1/3

C.4

D.3

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.

For the equation (m-2)x² + 5x - 7 = 0 to be a quadratic equation, what must be true about the value of m?

A.m = 2

B.m ≠ 2

C.m > 2

D.m can be any real number

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