Question

Write all values of k for which quadratic equation x²+kx+16=0 has equal roots Also find the roos of the equation so obtained

Answer 1

Equation: x^2 + kx + 16

Compare the given equation with ax^2 + bc + c,

Therefore, a = 1, b = k and c = 16

Now,

For equal roots Discriminant (D) = 0

=> b^2 - 4ac = 0

=> k^2 - 4(1)(16) = 0

=> k^2 - 64 = 0

=> k^2 = 64

=> k = ±8

Thus, the values of k for which the given equation has equal roots are +8 and -8.

Answer 2

For real roots, D = 0

k^2 - 4(1)(14) = 0

k^2 - 64 = 0

k^2 = 64

k = ±8