Advertisements
Advertisements
Question
If (x+a) is a factor of the polynomial `2x^2 + 2ax + 5x + 10`, find the value of a.
Solution
Given: (x + a) is a factor of `2x^2 + 2ax + 5x + 10`
So, we have
x + a = 0
⇒ x = –a
Now, it will satisfy the above polynomial.
Therefore, we will get
`2 (–a)^2 + 2a(–a) + 5(–a) + 10 = 0`
`⇒ 2a^2 –2a^2 – 5a + 10 = 0`
`⇒ – 5a = – 10`
`⇒ a = 2`
APPEARS IN
RELATED QUESTIONS
Find a quadratic polynomial each with the given numbers as the sum and product of its zeroes respectively.
`1/4 , -1`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate :
`a(α^2/β+β^2/α)+b(α/β+β/α)`
If α and β are the zeros of the quadratic polynomial f(x) = x2 − 1, find a quadratic polynomial whose zeroes are `(2alpha)/beta" and "(2beta)/alpha`
If α and β are the zeros of the quadratic polynomial f(x) = x2 − p (x + 1) — c, show that (α + 1)(β +1) = 1− c.
If If α and β are the zeros of the quadratic polynomial f(x) = x2 – 2x + 3, find a polynomial whose roots are `(alpha-1)/(alpha+1)` , `(beta-1)/(beta+1)`
Verify that 5, -2 and 13 are the zeroes of the cubic polynomial `p(x) = (3x^3 – 10x^2 – 27x + 10)` and verify the relation between its zeroes and coefficients.
What should be added to the polynomial x2 − 5x + 4, so that 3 is the zero of the resulting polynomial?
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
4x2 – 3x – 1
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
t3 – 2t2 – 15t
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`y^2 + 3/2 sqrt(5)y - 5`
