Question

Form an quadratic equation whose roots are 4+√7÷2&4-√7÷2

Answer 1

Let alpha and beta be two zeros of the polynomial.

GIVEN :-

$\alpha = 4 + \frac{ \sqrt{7} }{2} \\ \\ \beta = 4 - \frac{ \sqrt{7} }{2}$

TO FIND :- The polynomial

SOLUTION :-

$\alpha + \beta \\ \\ = 4 + \frac{ \sqrt{7} }{2} + 4 - \frac{ \sqrt{7} }{2} \\ \\ = 8$

$\alpha \beta \\ \\ = (4 + \frac{ \sqrt{7} }{2} )(4 - \frac{ \sqrt{7} }{2} ) \\ \\ \\ = {4}^{2} -{ ( \frac{ \sqrt{7} }{2} ) }^{2} \\ \\ = 16 - \frac{7}{4} \\ \\ = \frac{57}{4}$

To form the quadratic polynomial

use this formula,

$p(x) =k [ {x}^{2} - ( \alpha + \beta ) + \alpha \beta ] \\ \\ = k [ {x}^{2} - 8x + \frac{57}{4} ] \\ \\ = 4 {x}^{2} - 32x + 57$

Where, k = 4

[Ans]

Answer 2

Refer to the attachment..

Hope it helps! :)