Question

Q5. In a Quadric Polynomial. If sum of zeroes is 7 and product of zeroes is 10
find the Quadratic polynomial.
14​

Answer 1

EXPLANATION.

$\sf \: sum \: of \: zeroes \: = 7$

$\sf products \: of \: zeroes \: = 10$

As we know that,

General formula of quadratic equation.

$\sf \: {x}^{2} - ( \alpha + \beta )x + \alpha \beta$

Sum of zeroes of quadratic equation.

$\sf \: \alpha + \beta = \dfrac{ - b}{a}$

$\sf \: \alpha + \beta = 7$

Products of zeroes of quadratic equation.

$\sf \: \alpha \beta = \dfrac{c}{a}$

$\sf \alpha \beta = 10$

Put the value in equation, we get.

$\sf \: {x}^{2} - (7)x + 10$

$\sf {x}^{2} - 7x + 10$

Answer 2

Answer:

Given :-

• Sum of zeroes = 7
• Product of zeroes = 10

Solution :-

As we know that

$\sf \: {x}^{2} ( \alpha + \beta )x + \alpha \beta$

Sum of zeroes

$\sf \: \alpha + \beta = \dfrac{ - b}{a}$

$\sf \: \alpha + \beta = 7$

Product of zeroes

$\sf \: \alpha \times \beta = \dfrac{c}{a}$

$\sf \: \alpha \beta = 10$

$\sf \: {x}^{2} - (7)x + 10$

$\sf \: {x}^{2} - 7x + 10$