Question

find
a quadratic polynomial whose zeroes are
7 - 3 root 2and 7+3 root 2
​

Answer 1

Quadartic Formula=>x²-(sum of zeroes)x + (product of zeroes)

=>x²-14x+31

Hope it helps...

Answer 2

ANSWER:

• Quadratic polynomial = x²-14x+31

GIVEN:

• First zero (α ) = 7-3√2
• Second zero (β) = 7+3√2

TO FIND :

• A quadratic polynomial have zeros ; (7-3√2) , (7+3√2)

SOLUTION:

Quadratic polynomial when zeros are given:

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

Finding sum of zeros (α+β)

= (7-3√2)+(7+3√2)

= 14

(α+β) = 14

Finding product of zeros (αβ)

= (7+3√2)(7-3√2)

= (7)² -(3√2)²

= 49- 18

= 31

Now putting the values in eq(I) we get;

=> p(x) = x²-14x+31

NOTE:

Standard form of Quadratic polynomial.

• ax²+bx+c Where a is not equal to 0