Question

for what values of m will the equation (m+1)x^2+2(m+3)x+(m+8) =0 has equal roots?

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Answer 1

Answer:

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Class 10

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>>Quadratic Equations

>>Nature of Roots

>>For how many values of m will the equati

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For how many values of m will the equation (m+1)x

2

+2(m+3)x+(2m+3)=0 have equal roots?

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Correct option is A)

The given equation is (m+1)x

2

+2(m+3)x+(2m+3)=0

Here, a=(m+1),b=2(m+3) and c=(2m+3)

For equal roots,

Discriminant=0⇒b

2

−4ac=0

⇒[2(m+3)]

2

−4(m+1)(2m+3)=0

⇒[(m+3)]

2

−(m+1)(2m+3)=0

⇒m

2

+6m+9−2m

2

−5m−3=0

⇒−m

2

+m+6=0

⇒m

2

−m−6=0

It is a quadratic equation, so m will have two solution

∴ for 2 values of m , the equation has equal roots.