Question:
One of the zeroes of the polynomial $2 x^{2}+7 x-4$ is
(a) 2
(b) $1 / 2$
(c)-1
(d)- 2
Thinking Process
(i) Firstly, determine the factor by using splitting method.
(ii) Further, put the factors equals to zero, then determine the values of $x$.
Solution:
(b) Let p (x) = 2x2 + 7x-4
= 2x2 + 8x-x-4 [by splitting middle term]
= 2x(x+ 4)-1(x+ 4)
= (2x-1)(x+ 4)
For zeroes of p(x), put p(x) = 0=> (2x -1) (x + 4) = 0
=> 2x-1 = 0 and x+4 = 0
=> x = ½ and x = -4
Hence, one of the zeroes of the polynomial p(x) is ½.