Question

:) Find the value of k so that the quadratic equation kx(3x-10) +
25 =0 , has two equal roots
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Answer 1

Answer:

k=3

Step-by-step explanation:

$kx(3x - 10) + 25 = 0$

has two equal roots

$= 3kx ^{2} - 10kx + 25 = 0$

according to the formula

$\sqrt{(b ^{2} } - 4ac) = 0$

to have equal roots

a = 3k

b = -10k

c = 25

$\sqrt{ ({100k}^{2} } - 4 (3k)(25) = 0$

$\sqrt{ ({100k}^{2} } - 300k) = 0$

squaring on both sides we get

$100 {k}^{2} - 300k = 0$

100 k² =300k

$\frac{100 {k}^{2} }{k} = 300$

the k on denominator gets canceled with k²in numerator and it changes to k

which gives

$100k = 300$

therefore k=3

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