Please answer these Questions -
- What real number is to be subtracted from 3x3+10x2-14x+9 so that the polynomial x-1 divides it exactly.
- Find the condition which must be satisfied by the coefficient of polynomial x3-px2+qx-r, when sum of its two zeroes are 0.
- If product of the two zeroes is 4 of the polynomials 1. ax2-6x-6
4. If the zeroes of the given Polynomial 4x2-2x+k-4 are reciprocal to each other, then find k.
Given, f(x) = x3 - px2 + qx -r
Let a-d, a, a+d be the zeros of the polynomial f(x).
So, sum of zeros = a - d + a + a + d = -(-p)
⇒ 3a = p
⇒ a =
Since, a is a zero of the polynomial f(x). So, f(a) = 0
⇒ a3 - pa2 + qa - r = 0
⇒ is the required condition.
1) alpha x bta = c/a = -6/a = 4
-6/a = 4
Since the roots are reciprocal of each other. So the product of the roots is 1.
The given polynomial is
if A and (1/A) are the zeroes of the given polynomial f(x).
Hence, the value of k=8