Question

Find the values of k for quadratic equation 2x2 + kx + 3 = 0, so that they have two equal roots.

Answer 1

given,
2x^2+Kx+3
here it is in the form ax^2+bc+C=0
here a=2, b=K, c=3
if it has two equal roots. then ∆=0
b^2-4ac=0
k^2-4(2)(3)=0
k^2-24=0
k^2=24
k=√24
k=2√6

Answer 2

we have to find the values of k for quadratic equations 2x² + kx + 3 = 0 so that they have two equal roots.

we know, quadratic equation will be equal only when

discriminant, D = b² - 4ac = 0

on comparing 2x² + kx + 3 = 0 with general form of quadratic equation , ax² + bx + c = 0 we get, a = 2, b = k and c = 3

so Discriminant , D = (k)² - 4(2)(3) = 0

or, k² - 24 = 0

or, k = ± √24 = ±2√6

hence, the value of k = 2√6 or -2√6