Algebra — Practice

Question 1

Write the quadratic formula.

Accepted Answer

x = [ −b ± √(b² − 4ac) ] / 2a.

Question 2

Find the discriminant of 3x² + 5x − 2 = 0 and the nature of its roots.

Accepted Answer

Δ = 25 − 4(3)(−2) = 49 > 0 → real and distinct roots.

Question 3

Find the sum and product of the roots of x² − 7x + 10 = 0.

Accepted Answer

Sum = 7, Product = 10.

Question 4

Solve x² + 2x − 8 = 0 by factorisation.

Accepted Answer

(x + 4)(x − 2) = 0 → x = −4 or 2.

Question 5

State the condition for the product AB of two matrices to exist.

Accepted Answer

The number of columns of A must equal the number of rows of B.

Question 6

Find the nature of roots of x² − 4x + 4 = 0.

Accepted Answer

Δ = 16 − 16 = 0 → real and equal roots.

Practice — Algebra