If the quadratic equation mx² + 2x + m = 0 has two equal roots, then find the values of m.

The given quadratic equation is
mx2 + 2x + m = 0we have a = m ; b = 2 ; c = mD = b2 - 4ac = (2)2 - 4(m)(m) = 4 - 4m2For equal roots, D = 0⇒4 - 4m2 = 0⇒4m2 = 4⇒m2 = 1⇒m = ±1

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If the quadratic equation mx2 + 2x + m = 0 has two equal roots then find the value of m

If the equation m x2+2 x+m=0 is satisfied by only one real value of x, then the values of m are and

Solution

Let mx2 + 2x + m = 0 be a quadratic equation. Since, the equation is satisfied by only one real value of x Therefore, the roots are real and equal.
⇒Discriminant =0⇒b2-4ac=0⇒22-4mm=0⇒4-4m2=0⇒4m2=4⇒m2=1⇒m=±1

Hence, the values of m are 1 and −1.

Mathematics

RD Sharma (2020, 2021)
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If the quadratic equation mx² + 2x + m = 0 has two equal roots, then find the values of m.

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