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Short-answer type questions (S.A.) :
Prove that the quadratic equation `x^(2)-6x+5=0` have the roots 1 and 5.

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We have, `x^(2)-6x+5=0`
or, `x^(2)-(1+5)x+5=0`
or, `x^(2)-x-5x+5=0`
or, `x(x-1)-5(x-1)=0`
or, `(x-1)(x-5)=0`
`:.` Either x-1=0 or, x-5=0
`impliesx=1" "impliesx=5`.
`:.` 1 and 5 are the roots of `x^(2)-6x+5=0`.
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CALCUTTA BOOK HOUSE-QUADRATIC EQUATION IN ONE VARIABLE-EXERCISE-1.5
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  8. The product of the roots of the quadratic equation ax^(2)+cx+b=0 is .

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  9. The sum of the roots of the quadratic equation (2-sqrt3)x^(2)+x+1=0 is...

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  10. Find the quadartic equation whose one root is (3-sqrt2)

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  11. Find m, given that the difference of the roots of the equation 2x^2-12...

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  12. Find the quadartic equation whose sum of the roots is 2 and sum of the...

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  13. For what values of a, the roots of the quadratic equation x^(2)-(3a-1)...

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  14. Determine the nature of the roots of the qaudratic equation 3sqrt2x^(2...

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  15. If alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0, ...

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  16. If alphaandbeta be the roots of the quadratic equation 2x^(2)+2x-3=0, ...

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  20. If alphaand beta be the roots of the equation x^(2)+px+q=0, then find ...

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  21. Solve by applying Sreedhar Acharya's formula - (px-1)(qx+2)+r=0

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