Question

8) Write the quadratic equation whose
roote are 1 by root 2 1 by root 2 ​

Answer 1

☆ To find:-

A quadratic equation whose zeroes are 1/root2 and 1/root2.

☆ Now,

We know that standard form of a quadratic equation is:-

${\large{\blue{\boxed{=》\:ax²+bx+c\:=\:0}}}}$

☆ Also,

Sum of the zeroes,

${\large{\blue{\boxed{=\:-b/a}}}}$

☆ And,

Product of the zeroes,

${\large{\blue{\boxed{=\:c/a}}}}$

☆ Therefore,

=》 1/root2 + 1/root2

= 2/root2

= 2/root2 × root2/root2

{Rationalizing}

=2root2/2

= root2

☆ And,

=》 1/root2 × 1/root2

= 1/2

▪︎ Therefore the Quadratic Equation,

=》 k{x²-(sum of the zeroes)x+product of the zeroes} = 0

Where k is constant.

=》 x²-(root2)x+1/2 = 0

= 2x²-2root2+1 = 0

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