Question

Find zeros of the quadratic polynomial x2 - 7x -8 and verify the relationship between zeros and coefficient

Answer 1

Answer:

x = 8 or -1 are the zeroes of the polynomial f(x) = x² - 7x - 8.

Step-by-step explanation:

Assumption,

Let the given polynomial be f(x)

Given,

The polynomial x² - 7x - 8

To find,

The zeroes of the polynomial f(x) = x² - 7x - 8

Calculation,

To find the zeroes of the polynomial f(x), we have to equate the polynomial to zero.

i.e. f(x) = 0

⇒ x² - 7x - 8 = 0

⇒ x² - 8x + x - 8 = 0 (Writing -7x as -8x + x)

⇒ x(x - 8) + 1(x - 8) = 0

⇒ (x - 8)(x + 1) = 0

i.e. x = 8 or -1 are the zeroes of the polynomial f(x) = x² - 7x - 8.

Verification,

If we compare f(x) with the general polynomial ax² + bx + c with α, and β as their zeroes. Then,

We get a = 1, b = -7, c = -8, α = 8, and β = -1

And we know that,

α + β = -b/a, and αβ = c/a  

⇒ 8 + (-1) = (-7)/1, and (8)(-1) = -8/1

⇒ -7 = -7, and -8 = -8

Therefore, as the L.H.S equals R.H.S the relationship between the zeroes and the constants of f(x) is justified.

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