Question

Write the value of k for which the quadratic equation x² − kx + 4 = 0 has equal roots.

Answer 1

SOLUTION :  

Given : x² - kx + 4 = 0  has equall roots.

On comparing the given equation with ax² + bx + c = 0  

Here, a = 1 , b = - k  , c = 4

D(discriminant) = b² – 4ac

D = (- k)² - 4 × 1 × 4

D = k² - 16  

D = 0 (Given : equal roots )

k² - 16 = 0

k² = 16

k = √16  

k = ± 4

Hence, the value of k is ± 4 .

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Answer 2

if the equation has equal roots then,
d=0
now
d = b^2 - 4ac
b = -k
c = 4
a = 1
d = {-k}^2 -4×1×4
d= k^2-16
0 = k^2 - 16
16 = k^2
√16= k
k = 4