Answer:
The zeros of the given polynomial \(6x^2-11x-10=0\) are \(\frac{5}{2}\) and \(\frac{-2}{3}\) .
Step-by-step explanation:
Consider the given polynomial,
\(6x^2-11x-10=0\)
We have to find the zeros of the given quadratic equation,
Solving using middle term splitting method,
-11x can be written as a sum of -15x and 4x and it will given product as -60.
The equation thus can be written as,
\(6x^2-11x-10=0\)
\(\Rightarrow 6x^2+4x-15x-10=0\)
\(\Rightarrow 2x(3x+2)-5(3x+2)=0\)
\(\Rightarrow (2x-5)(3x+2)=0\)
\(\Rightarrow x=\frac{5}{2}\) and \(\Rightarrow x=\frac{-2}{3}\)
Zeros satisfies the polynomial , when we put them back in the equation, it must give result as zero.
Thus, the zeros of the given polynomial \(6x^2-11x-10=0\) are \(\frac{5}{2}\) and \(\frac{-2}{3}\)
