Question

find the zeros of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients x square -x -72​

Answer 1

Solution:-

Given:-

• Polynomial :- x² - x - 72.

To Find:-

• Two Zeroes = ?

Find:-

=) x² - x - 72

=) x² - ( 9 - 8)x - 72

=) x² - 9x + 8x - 72

=) x ( x - 9) +8 ( x - 9)

=) ( x -9) ( x + 8)

=) [ x = 9 ] and [ x = -8 ]

Let [ α = 9 ] and [ β = -8 ]

Verification:-

• Sum of the Zeroes = -b/a

=) α + β = -b/a

=) 9 + (-8) = - (-1)/1

=) 1 = 1

L.H.S. = R.H.S.

• Product of Zeroes = c/a

=) αβ = c/a

=) 9 × (-8) = -72/1

=) -72 = -72

L.H.S = R.H.S.

Hence Verified!

Answer 2

Answer :-

To find the zeroes, firstly Factorise it by mid-term splitting method ;

x² - x - 72

=) x² - 9x + 8x - 72

=) x (x - 9) + 8 (x - 9)

=) (x + 8) (x - 9)

(x + 8) = 0

=) x = -8

(x - 9) = 0

=) x = 9

So, the two zeroes are -8 and 9.

Verification :-

Sum of zeroes = -b/a

= 9 + (-8) = -(-1)/1

= 1 = 1

Also, Product of zeroes = c/a

= -8 × 9 = -72/1

= -72 = -72

Hence, Verified !!