CBSE 10 - Maths
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Asked by navneetpra499 | 19 Jul, 2022, 05:06: AM
CBSE 10 - Maths
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Asked by anuragtikekar2006 | 07 May, 2022, 06:33: PM
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CBSE 10 - Maths
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Asked by Vadderamakrishna2 | 30 Aug, 2021, 12:17: PM
ANSWERED BY EXPERT
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