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प्रश्न
If one of the equation ax2 + bx + c = 0 is three times times the other, then b2 : ac =
पर्याय
3 : 1
3 : 16
16 : 3
16 : 1
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उत्तर
Let `alpha and beta`be the roots of quadratic equation`ax^2 + bx + c = 0` in such a way that `alpha = 3beta`
Here, a = a, b = b and , c = c
Then,
according to question sum of the roots
`alpha + beta = (-b)/a`
`3 beta + beta = (-b)/a`
`4beta = (-b)/a`
`alpha = (-b)/(4a)`….. (1)
And the product of the roots
`alpha . beta = c/a`
`3beta xx beta = c / a`
`3beta^2 = c/a`
`beta^2 = c /3a`….. (2)
Putting the value of `beta = (-b)/(4a)` in equation (2)
`(-b)/(4a)^2 = c /(3a)`
`(b^2)/(16a^2) = c/3a`
`b^2 = c/(3a) xx 16a^2`
`b^2 = (16ac)/3`
`b^2 / (ac) = 16/3`
`b^2 : ac = 16 :3`
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