Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Write the standard form of a quadratic equation. ax2+bx+c=0ax+b=0ax2=cax3+bx=0

(2) What is the discriminant of the equation x2 - 4x + 4 = 0?

Correct! Discriminant = b2 - 4ac = −42 - 4(1)(4) = 16 - 16 = 0.

(3) Write the sum and product of the roots of the equation x2 - 5x + 6 = 0. Sum = and Product =

Perfect! For ax2 + bx + c = 0, sum = −ba = 5 and product = ca = 6.

(4) What is the nature of the roots of x2 + 2x + 1 = 0? Equal and realDistinct and realComplexIrrational

Excellent! Discriminant = 4 - 4 = 0, so roots are equal and real.

Short Answer Questions (2 Marks Each)

(1) Solve x2 - 7x + 10 = 0 by factorization method. x = ,

Perfect! x2−7x+10 = (x - 2)(x - 5) = 0, so x = 2 or x = 5.

(2) Find the quadratic equation whose roots are 2 and 3. Equation is x2 + + = 0

Excellent! Using (x - α)(x - β) = 0: (x - 2)(x - 3) = x2 - 5x + 6 = 0.

(3) Solve x2 - 9 = 0. x = and

Perfect! x2 = 9, so x = ± 9 = ± 3.

(4) If x2 = 4x + 5, convert it into standard form and solve. Standard form: x2−4x−5x2+4x+5 = 0 with roots x = and

Excellent! Rearranging: x2 - 4x - 5 = 0, factoring: (x - 5)(x + 1) = 0.

Long Answer Questions (4 Marks Each)

(1) Derive the formula to solve a quadratic equation.

(2) A number is divided into two parts such that their product is 56 and their difference is 3. Find the number. The number is

Perfect! Let the parts be x and y. Then xy = 56 and x - y = 3. Solving: x = 8, y = 7, so the number = 8 + 7 = 15.

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) If one root of the equation ax2+bx+c = 0 is double the other, then the value of b2 is:

(a) 2ac (b) 4ac (c) a2c2 (d) a2+4ac

Correct!

(2) The roots of x2 - 4x + 4 = 0 are

(a) 2, 2 (b) -2, -2 (c) 2, -2 (d) 0, 4

Correct! x2 - 4x + 4 = x−22 = 0, so x = 2 (repeated root).

(3) The discriminant of x2 + 2x + 1 = 0 is

(a) 1 (b) 0 (c) 4 (d) -2

Correct! Discriminant = b2 - 4ac = 4 - 4(1)(1) = 0.

(4) The product of roots of x2 - 5x + 6 = 0 is

(a) -5 (b) 6 (c) -6 (d) 5

Correct! Product of roots = ca = 61 = 6.

(5) The roots of x2 - 9 = 0 are

(a) 3, 3 (b) -3, 3 (c) 9, -9 (d) 0, 9

Correct! x2 = 9 gives x = ±3.

(6) If the roots of x2 + kx + 9 = 0 are equal, then k =

(a) 0 (b) ±6 (c) ±3 (d) ±2

Correct! For equal roots, discriminant = 0: k2 - 36 = 0, so k = ±6.

(7) If one root of a quadratic equation is 2 and the other is 3, the equation is

(a) x2 + 5x + 6 = 0 (b) x2 - 5x + 6 = 0 (c) x2 + 5x - 6 = 0 (d) x2 - 6x + 5 = 0

Correct! (x - 2)(x - 3) = x2 - 5x + 6 = 0.

(8) The sum of the roots of x2 - 3x + 2 = 0 is

(a) 3 (b) -3 (c) 2 (d) 5

Correct! Sum of roots = −ba = −−31 = 3.

(9) The graph of a quadratic equation is a

(a) Line (b) Parabola (c) Circle (d) Ellipse

Correct! Quadratic functions always form parabolic curves.

(10) Which of these is NOT a quadratic equation?

(a) x2 + 2x + 3 = 0 (b) x + 2 = 0 (c) x2 - 1 = 0 (d) 3x2 = 4x - 5

Correct! x + 2 = 0 is linear (degree 1), not quadratic (degree 2).

Quadratic Equations Challenge

Determine whether these statements about quadratic equations are True or False:

Quadratic Equations Quiz