Advertisements
Advertisements
Question
If (a-b) , a and (a + b) are zeros of the polynomial `2x^3-6x^2+5x-7` write the value of a.
Solution
By using the relationship between the zeroes of the quadratic polynomial.
We have
Sum of zeroes = `(-("Coefficient of" x^2))/("Coefficient of "x^3)`
`a – b + a + a + b =(-(-6))/2`
⇒ 3a = 3
⇒ a = 1
APPEARS IN
RELATED QUESTIONS
Check whether the first polynomial is a factor of the second polynomial by dividing the second polynomial by the first polynomial
x3 – 3x + 1, x5 – 4x3 + x2 + 3x + 1
If the polynomial x4 – 6x3 + 16x2 – 25x + 10 is divided by another polynomial x2 – 2x + k, the remainder comes out to be x + a, find k and a.
Apply division algorithm to find the quotient q(x) and remainder r(x) on dividing f(x) by g(x) in the following f(x) = 15x3 − 20x2 + 13x − 12; g(x) = x2 − 2x + 2
What must be subtracted from the polynomial f(x) = x4 + 2x3 − 13x2 − 12x + 21 so that the resulting polynomial is exactly divisible by x2 − 4x + 3 ?
Find all the zeros of the polynomial 2x3 + x2 − 6x − 3, if two of its zeros are `-sqrt3` and `sqrt3`
State Division Algorithm for Polynomials.
Find the quotient and remainder of the following.
(4x3 + 6x2 – 23x + 18) ÷ (x + 3)
Find the quotient and remainder of the following.
(−18z + 14z2 + 24z3 + 18) ÷ (3z + 4)
Which one of the following statements is correct?
Can x2 – 1 be the quotient on division of x6 + 2x3 + x – 1 by a polynomial in x of degree 5?
