Question

1.
1. Form a quadratic equation if its roots are
and
1/2 and - 3/4​

Answer 1

Step-by-step explanation:

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Answer 2

Given :-

• roots of equation are 1/2 and -3/4

To Find :-

• quadratic equation ?

Solution :-

here,

$\bold{sum \: of \: zeroes = \frac{1}{2} + \frac{ - 3}{4} } \\ \\ \bold{: \implies \frac{2 - 3}{4} } \\ \\ \bold{: \implies - \frac{1}{4} } \: \: \: \: \:$

and

$\bold{product \: of \: zeroes = \frac{1}{2} \times \frac{ - 3}{4} } \\ \\ \bold{: \implies - \frac{3}{8} }$

and we know that,

quadratic equation = x² - (sum of zeroes )x + product of zeroes

$\boxed{ \bold{ {x}^{2} - (sum \: of \: zeroes)x + (product \: of \: zeroes)}}$

$\bold{: \implies {x}^{2} - \bigg( - \frac{1}{4} \bigg) x+ \bigg( - \frac{3}{8} \bigg) = 0} \\ \\ \bold{ : \implies {x}^{2} + \frac{1}{4} x - \frac{3}{8} = 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies \frac{8 {x}^{2} + 2x - 3}{8 } = 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \bold{: \implies 8 {x}^{2} + 2x - 3 = 0} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

hence, the quadratic equation is 8x² + 2x - 3