If one of the root of the quadratic equation px² 15x 14 0 is 2/3 find the value of p

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Asked by navneetpra499 | 19 Jul, 2022, 05:06: AM

CBSE 10 - Maths

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CBSE 10 - Maths

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Asked by Vadderamakrishna2 | 30 Aug, 2021, 12:17: PM

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Find the value of p, for which one root of the quadratic equation px2 – 14x + 8 = 0 is 6 times the other.

Let the first root be α, then the second root will be 6α.

Sum of roots= `(−b)/a`

`=> a + 6a = 14/p`

`=> 7a = 14/p`

`=> a = 2/p`

Product of roots = `c/d`

`=> a  xx  6a = 8/p`

`=> 6a^2 = 8/p`

`=>6(2/p)^2 = 8/p`

`=> p = 3`

Hence the value of p is 3

Concept: Nature of Roots of a Quadratic Equation

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Given quadratic equation is, px² -2√5 px + 15 = 0

Compare px² -2√5 px + 15 = 0 with ax² + bx + c = 0

a = p , b = -2√5p , c = 15

We know that , If the roots of the quadratic equation are equal , then it's discriminant (D) equals to zero.discriminant = 0b² - 4ac = 0( -2√5 p )² - 4× p × 15 = 020p² - 60p = 020p ( p - 3 ) = 0p - 3 = 0

p = 3