Question

Verify whether 3 and 2 are the zeros of the poly. (x-2) (x-3)?

Answer 1

Heya !!!




P(X) = (X-2)(X-3)





=> X(X-3) - 2(X-3)





=> X²-3X-2X+6




=> X²-5X+6






P(X) = X²-5X+6




P(3) = (3)²- 5 × 3 + 6



=> 9 - 15 + 6




=> 15-15



=> 0






P(X) = X²-5X+6





P(2) = (2)² - 5 × 2 + 6





=> 4 - 10 + 6




=> 10-10




=> 0





In both the cases remainder is equal to 0.




Hence,




3 and 2 are the zeroes of the quadratic polynomial (X-2)(X-3).





★ HOPE IT WILL HELP YOU ★

Answer 2

Hy!!
____________
Let the zeroes are 3 and 2

$p(x) = (x - 2)(x - 3) \\ \: \: \: \: \: \: \: \: \: \: = x(x - 3) - 2(x - 3) \\ \: \: \: \: \: \: \: \: \: \: = x {}^{2} - 3x - 2x + 6 \\ \: \: \: \: \: \: \: \: \: \: \: = x {}^{2} - 5x + 6 \\ \\ p(x) = x {}^{2} - 5x + 6 \\ \: p(3)= 3 {}^{2} - 5(3) + 6 \\ \: \: \: \: \: \: \: \: \: \: \: = \: 9 - 15 + 6 \\ \: \: \: \: \: \: \: \: \: \: \: \: = 0 \\ \\ p(x) = x {}^{2} - 5x + 6 \\p(2) = 2 {}^{2} - 5(2) + 6 \\ \: \: \: \: \: \: \: \: \: \: = 4 - 10 + 6 \\ \: \: \: \: \: \: \: \: \: \: \: = 0$

3 and 2 are the zeroes of the quadratic polynomial (x-2)(x-3)

Hope it will helps you:-)