Question

Find the values of k for which the equation x^2 + 5kx + 16 = 0 has real and equal roots.

Answer 1

(i) Interpret the equation:

For roots to be real and equal, we need to solve for the value of k such that Δ = 0.

(ii) Check that the equation is in standard form ax^2 + bx + c = 0.

x^2 + 5kx + 16 = 0

(iii) Identify the coefficients to substitute into the formula for discriminant

a = 1, b = 5k, c = 16.

(iv) Write down the formula and substitute values:

⇒ b^2 - 4ac = 0

⇒ (5k)^2 - 4(1)(16) = 0

⇒ 25k^2 - 64 = 0

⇒ 25k^2 = 64

⇒ k^2 = 64/25

⇒ k = √64/25

⇒ k = +8/5, -8/5.

Hope it helps!