Question

If two zeroes of the polynomial 2(x^4)+(x^3)-14(x^2)-19x-6 are -2 and -1 , then the other zeroes are

1 point

3 and 1/2

-3 and -1/2

-3 and 1/2

3 and -1/2​

Answer 1

Answer:

So you have two roots for a biquadratic equation and required to find the other two. As only the formula to find roots of a quadratic equation is given to you. You first have to convert the biquadratic polynomial to a quadratic polynomial.

For doing that,

Step-1

Form a quadratic equation by using the roots given(α + β = - ba and αβ = ca use these two conditions to find a, b and c. Then fill the values of found a,b, and c in x2 + bax + ca = 0 (Since, a ≠ 0))

Step-2

Now divide the biquadratic polynomial with the quadratic polynomial you have just formed. (use long division method)

Step-3

Now you will get a quadratic equation as your quotient form the long division. The roots of that quotient will be the required roots.