Question

If α,β are the zeros of the polynomial, x sq-px +36 and α sq + β sq = 9, then what is the value of p? *

1 point

6

9

3

8

​

Answer 1

ANSWER:

SO THE VALUE OF P = 9 OR (-9)

GIVEN:

α and β are the two zeros of polynomial

$x {}^{2} - px + 36$

TO FIND:

Value of 'p'

SOLUTION:

Here;. a= 1 (coefficient of x^2) b= (-p) (coefficient of x)

c= 36 (constant term)

$\implies \: \alpha + \beta = \frac{( - b)}{a} \\ \implies \: \alpha + \beta= \: \frac{ - ( - p)}{1} \\ \implies \: \alpha + \beta= p \\ \\ \implies \: \alpha \times \beta = \frac{c}{a} \\ \implies \: \alpha \times \beta = \frac{36}{1} \\ \implies \: \alpha \times \beta= 36$

Formula

$\implies \: x {}^{2} + y {}^{2} = (x + y) {}^{2} - 2xy$

By using this formula:

$\implies \: \alpha{}^{2} +\beta {}^{2} = 9 \: \: \: \: \: (given) \\ \implies \: (\alpha+ \beta) {}^{2} - 2\alpha\beta = 9 \\ \: \: \: \: \: putting \: the \: values \: we \: get \\ \implies \: (p) {}^{2} - 2 \times 36 = 9 \\ \implies \: (p) {}^{2} = 9 + 72 \\ \implies \: p \: = \sqrt{81} \\ \implies \: p = 9 \: or \: ( - 9)$

SO THE VALUE OF P = 9 OR (-9)

NOTE:

• First of all we have to find the value of α+β and αβ.
• Then put on the formula above given.
• simplify it and find the value.