Question

Zeroes of the polynomial y^2-9y+20 are *

Answer 1

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y²-9y+20

y²-4y-5y+20

y( y-4 ) - 5( y - 4 )

(y - 4 ) ( y - 5 )

Answer 2

Given :

Polynomial

$y {}^{2} - 9y + 20$

What to find out : zeroes of the poynomial?

Solution:

Concept :

Factorization of Quadratic polynomials of the form x^2 + bx + c.

(i) In order to factorize x^2 + bx + c we have to find numbers p and q such that p + q = b and pq = c.

(ii) After finding p and q, we split the middle term in the quadratic as px + qx and get desired factors by grouping the terms.

Answer

In order to factorize y^2 - 9x + 20, we find two numbers p and q such that p + q = - 9and pq =20

Clearly, [(-5) + (- 4) ]= - 9and (-5) ×(-4) = 20

We know split the middle term :-

Y^2-9y+20= y^2-5y-4y+20

= y(y-5)-4(y-5)

Take out common term

=(y-5)(y-4)

Hence, the zeroes of the poynomial = 5 and 4