If the quadratic equation px2 ndash- 2 5 px - 15 - 0 has two equal roots-then find the value of p-

The #160;equation #160;px2 25px+15=0 #160;has #160;equal #160;roots, #160;then #160;D=0. 25p2 4 #215;p #215;15=0 #8658;625p2 60p=0 #8658;5 ...

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Standard XII

Mathematics

Nature of Roots

If the quadra...

Question

If the quadratic equation px2 – 2 5 px + 15 = 0 has two equal roots,
then find the value of p.

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Solution

$The equation {px}^{2} - 25 px + 15 = 0 has equal roots, then D = 0 . {(- 25 p)}^{2} - 4 \times p \times 15 = 0 \Rightarrow 625 p^{2} - 60 p = 0 \Rightarrow 5 p (125 p - 12) = 0 \Rightarrow p = 0 or 125 p - 12 = 0 \Rightarrow p = 0, \frac{12}{125}$

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Q. If −5 is a root of the quadratic equation

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and the quadratic equation

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has equal roots, find the value of k.

If $- 5$ is a root of the quadratic equation $2 x^{2} + p x - 15 = 0$ and the quadratic equation $p (x^{2} + x) + k = 0$ has equal roots, find the value of $k$ .

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If the quadratic equation px2 – 2 5 px + 15 = 0 has two equal roots, then find the value of p.

The equation px2-25px+15=0 has equal roots, then D=0.-25p2-4×p×15=0⇒625p2-60p=0⇒5p125p-12=0⇒p=0 or 125p-12=0⇒p=0, 12125

If the quadratic equation px2 – 2 5 px + 15 = 0 has two equal roots,
then find the value of p.

$The equation {px}^{2} - 25 px + 15 = 0 has equal roots, then D = 0 . {(- 25 p)}^{2} - 4 \times p \times 15 = 0 \Rightarrow 625 p^{2} - 60 p = 0 \Rightarrow 5 p (125 p - 12) = 0 \Rightarrow p = 0 or 125 p - 12 = 0 \Rightarrow p = 0, \frac{12}{125}$