Question

Please solve both the questions.

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Answer 1

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Answer 2

ANSWER :–

(1) Given :–

• A QUADRATIC EQUATION WHICH HAVE

HAVE TWO ROOTS .

• SUM OF ROOTS = √2

• PRODUCT OF ROOTS = -3/2

☆TO FIND☆ :–

QUADRATIC EQUATION

SOLUTION :–

● WE KNOW A EQUATION WHEN SUM OF ROOTS

AND PRODUCT OF ROOTS HAS GIVEN.

● EQUATION =》

X² - (SUM OF ROOTS) X +(PRODUCT OF ROOTS) = 0

SO THAT , EQUATION =》

=》 X² - √2 x - 3/2 = 0

NOW FIND IT'S ROOTS =》

${ \bold{x = \frac{ - \sqrt{2} + \sqrt{2 - 4( - \frac{3}{2} )} }{2} \: \: and \: \: x = \frac{ - \sqrt{2} - \sqrt{2 - 4( - \frac{3}{2} )} }{2} }} \\ \\ { \bold{{x = \frac{ - \sqrt{2} + \sqrt{8} }{2} \: \: and \: \: x = \frac{ - \sqrt{2} - \sqrt{8} }{2} }}} \\ \\{ \bold{x = \frac{ -1 + 2 }{ \sqrt{2} } \: \: and \: \: x = \frac{ - 1 - 2}{ \sqrt{2} } }} \\ \\ { \bold{ x = \frac{1}{ \sqrt{2} } \: \: and \: \: x = - \frac{3}{ \sqrt{2} } }}$

(2) GIVEN QUADRATIC EQUATION :–

=》 X² + (1/6) X - 2 = 0

TO FIND :–

ROOTS OF QUADRATIC EQUATION.

SOLUTION :–

=》 6 x² + x - 12 = 0

• NOW FACTORIES —

=》 6 X² + 9 X - 8X - 12 = 0

=》3 X ( 2X + 3 ) - 4 ( 2X + 3 ) = 0

=》 ( 3X - 4 ) ( 2X +3 ) = 0

=》 X = 4/3 , X = -3/2

$sum \: \: of \: \: roots \: = - \frac{b}{a} = - \frac{1}{6} \\ \\ product \: \: of \: \: roots \: = - 2$