Question

Find the value(s) of ‘k' for which the equation 2x2- kx +k = 0 has real and equal roots.

Answer 1

If this equation has real and equal roots.
since b^2-4ac=0
in this equation-
a=2
b=-k
c=k
thus. -k^2-4*2k=0
k^2-8k=0
k(k-8)=0
k=0
k-8=0
k=8

Answer 2

Answer:

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

or

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