Question

Which are zeros of the following polynomial? 6x 2 - 11x - 10 = 0

Answer 1

The zeros of the given polynomial
`6x^2-11x-10=0` are
`(5)/(2)` and
`(-2)/(3)` .

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=(5)/(2)` and
`\Rightarrow x=(-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
`(5)/(2)` and
`(-2)/(3)`

Answer 2

Hello,

0=6x²-11x-10=6x²-15x+4x-10=3x(2x-5)+2(2x-5)=(2x-5)(3x+2)

Zeroes are: x=5/2 and x=-2/3