Question

If zeros alpha and beta of a polynomial x square - 7 x + K such that Alpha minus beta is equal to 1 then find the value of k

Answer 1

This is ur answer. Hope u got it

Answer 2

The value of k is 12.

Step-by-step explanation:

If a polynomial is $P(x)=ax^2+bx+c$, then

Sum of zeros = -b/a

Product of zeros = c/a

The given polynomial is

$P(x)=x^2-7x+k$

It is given that α and β are zeros of the given polynomial.

Here, a=1, b=-7 and c=k.

$\alpha+\beta=-\frac{-7}{1}$

$\alpha+\beta=7$               ... (1)

$\alpha\beta=\frac{k}{1}$

$\alpha\beta=k$        ... (2)

It is given that

$\alpha-\beta=1$             ... (3)

On adding (1) and (3) we get

$2\alpha=8$

$\alpha=4$

Substitute $\alpha=4$ in equation (1).

$4+\beta=7$

$\beta=3$

Substitute $\alpha=4$ and $\beta=3$ in equation (2).

$(4)(3)=k$

$12=k$

Therefore, the value of k is 12.

#Learn more

If the sum of zeroes of polynomial p(x)=2x^2-kx+4is the same as the product of zeroes find the value of k.

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