Find the zeros of the following quadratic polynomials :
(1) p(x) = x2 + 4x - 21
(2) p(x) = 6x2 - 11x + 5
(3) p(x) = 4x2 + 9x + 5
(4) p(x) = 3x2 + 5x - 8
(5) p(x) =x2- 81
(6) P(x) = x^2-x-6
Answers
1)
p(x) = x² + 4x - 21
==> x² + 4x - 21 = 0
==> x² + 7x - 3x - 21 = 0
==> x(x + 7) - 3( x + 7) = 0
==> (x + 7)(x - 3) = 0
Zeroes are -7 and 3
2)
p(x) = 6x² - 11x + 5
==> 6x² - 11x + 5 = 0
==> 6x² - 6x - 5x + 5 = 0
==> 6x ( x - 1) - 5(x - 1) = 0
==> (x - 1)(6x - 5) = 0
Zeroes are 1 and 5/6
3)
p(x) = 4x² + 9x + 5
==> 4x² + 4x + 5x + 5 = 0
==> 4x( x + 1) + 5( x + 5) = 0
==> (x + 1)(4x + 5) = 0
Zeroes are -1 and -5/4
4)
p(x) = 3x² + 5x - 8
==> 3x² - 3x + 8x - 8 = 0
==> 3x( x - 1) + 8 ( x - 1) = 0
==> (x - 1)(3x + 8) = 0
Zeroes are 1 and -8/3
5)
p(x) = x² - 81
==> x² - 81 = 0
==> x² - 9² = 0
==> (x + 9)(x - 9) = 0
Zeroes are 9 and -9
6)
p(x) = x² - x - 6
==> x² + 2x - 3x - 6 = 0
==> x( x + 2) - 3(x + 2) = 0
==> (x + 2)(x - 3) = 0
Zeroes are 3 and -2