Question

Find the quadratic polynomial, the sum of whose zeros is -5 and the product is 6

Answer 1

Answer:

Given that the sum and product of zeros of quadratic polynomial are 8 and 12, respectively.  Therefore, x1 + x2 = 8 ⇒ x2 = 8 – x1   ... (1)  And x1 x2 = 12.   ... (2)  Now, putting the value of x2, from equation (1) into equation (2),  we get  x1(8 − x1) = 12 ⇒ 8x1 – x12 = 12  ⇒ x12 − 8 x1+ 12 = 0 ⇒ (x1 − 2)(x1 − 6) = 0  ⇒ x1 = 2 or x1 = 6. Now, putting the value of x1 into equation (1), we get  If x1 =2, then x2 = 8 – 2 = 6.  If x1 = 6, then x2 = 8 – 6 = 2.  Hence, the zeros of quadratic polynomial are 2 and 6.Read more on Sarthaks.com - https://www.sarthaks.com/1106437/find-the-quadratic-polynomial-whose-zeros-and-their-product-hence-find-zeros-polynomial

Answer 2

Answer:

We know that, general formula of quadratic equation is :

$\sf \: {x}^{2} - (sum \: of \: zeroes \: )x + product \: of \: zeroes = 0 \\ \\ \bf \: and \: polynomial \: is \: \\ \\ \sf {x}^{2} - (sum \: of \: zeroes)x + product \: of \: zeroes$

Now given,

A quadratic polynomial, whose

sum of zeroes is = -5 and

product of zeroes is = 6

So the polynomial is n

$\sf \: {x}^{2} - ( - 5)x + 6 \\ \sf \: = {x}^{2} + 5x + 6$