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Obtain a quadratic equation whose roots...

Obtain a quadratic equation whose roots are -3 and -7.

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The correct Answer is:
The required quadratic equation is `x^(2) + 10x + 21 = 0`
Let `alpha = - 3` and `beta = - 7`
Then `alpha + beta = - 3-7 = -10` and `alpha beta = ( -3) xx ( -7) = 21 `
The required quadratic equation is
`x^(2) - (alpha + beta) x + alpha beta = 0 `
`:. x^(2) - ( -10) x + 21 = 0`
`:. x^(2) + 10x + 21 = 0` ....( Substituting the values )
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