Question

find the zeros of the polynomial for the following quadratic polynomial P of x is equal to 6 x square - 3 - 7 x​

Answer 1

Step-by-step explanation:

◾This is an qudractic polynomial

◾To find its zeroes equate it to zero

◾This can be solved by two methods

1]. Middle-term splitting :-

$f(x) = 6 {x}^{2} - 7x - 3 = 0 \\ \\ 6 {x}^{2} + 2x - 9x - 3 = 0 \\ \\ 2x(3x + 1) - 3(3x + 1) = 0 \\ \\ (2x - 3)(3x + 1) = 0$

$\\ \\ 2x - 3 = 0 \\ \\ x = \frac{3}{2}$

$3x + 1 = 0 \\ \\ x = - \frac{1}{3}$

2]. Using quadratic formula

$x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a}$

a,b,c are the respective coefficients

applying formula

$\frac{ - ( - 7) \pm \sqrt{49 - 4 \times 6 \times ( - 3)} }{2(6)} \\ \\ \frac{7 \pm \sqrt{49 + 72} }{12} \\ \\ \frac{7 \pm \sqrt{121} }{12} \\ \\ \frac{7 \pm 11}{12}$

$= \frac{7 + 11}{12} \\ \\ = \frac{18}{12} \\ \\ = \frac{3}{2} \\ \\ = \frac{7 - 11}{12} \\ \\ = \frac{ - 4}{12} \\ \\ = - \frac{1}{3}$