Question

WIUWI UN
26.) Find the value of k:
(i) If a and B are the zeros of the polynomial
x2 - 8x + k such that a2 + B2 = 40.
​

Answer 1

Polynomial Rules

• a + ß = - Coefficient of x/Coefficient of x²
• aß = Constant Term/Coefficient of x²

______________________________

➵ a + ß = - (- 8)/1

➵ a + ß = 8 __[1]

➵ aß = k/1

➵ aß = k

______________________________

On squaring eq [1] we get,

➵ a² + ß² + 2aß = 64

Since a² + ß² = 40 [Given] and aß = k.

➵ 40 + 2k = 64

➵ k = 24/2

➵ k = 12

______________________________

Hence value of k is 12.

$\huge{\boxed{\bold{k = 12}}}$

Answer 2

Answer:

12

Step-by-step explanation:

Given Polynomial,

x² - 8x + k

Here, as compared to the general form of a quadratic equation (ax² + bx + c), we get

a = 1

b = -8

c = k

Given that zeroes of the polynomial are $\sf \alpha \ and \ \beta$

We know that, sum of zeroes =

- (b)/a

and, product of zeroes = c/a

So, $\sf \alpha + \beta = \frac{-(b)}{1} \\ \\ \implies \frac{-(-8)}{1} \\ \\ \implies \alpha + \beta = 8$

and, $\sf \alpha\beta = \frac{c}{a} = \frac{k}{1} \\ \\ \implies \alpha\beta = k$

Now, $\sf \alpha^2 + \beta^2$ can be written as :-

$\sf \alpha^2 + \beta^2= (\alpha + \beta)^2 - 2\alpha\beta \\ \\ \implies 40 = (8)^2 - 2k \\ \\ \implies 40 = 64 - 2k \\ \\ \implies -2k = 40 - 64 \\ \\ \implies -2k = -24 \\ \\ \implies k = \frac{-24}{-2} \\ \\ \implies k = 12$