Question

☆ Topic : Quadratic Equations

Find the value of k for each of the following quadratic equations, so that they have two equal roots.

$1. \: \sf 2 {x}^{2} + kx + 3 = 0$
$\sf \: 2. \: kx(x - 2) + 6 = 0$
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Answer 1

(1) 2x²+kx+3=0

a(co-efficient of x²)=2

b(co-efficient of x)=k

c(the constant value)=3

D=b²–4ac

D=k²–4*2*3

D=k²–24

FOR EQUAL ROOTS”D” MUST BE EQUAL TO ZERO

D=0

k² -24=0

ADDING 24 TO BOTH SIDES

k²–24+24=24

k²=24

k=√24

k=±2√6