Advertisements
Advertisements
प्रश्न
If x + 2 is a factor of x2 + ax + 2b and a + b = 4, then
पर्याय
a= 1, b = 3
a = 3, b = 1
a = −1, b = 5
a = 5, b = −1
Advertisements
उत्तर
Given that x + 2 is a factor of `x^2 + ax + 2b` and a + b=4
`f(x)=x ^2 +ax + 2b`
`f(-2)= (-2)^2 +a(-2 )+ 2b`
`0 = 4-2a +2b`
`-4 = -2a+2b`
By solving `-4 = -2a+2b` and a + b = 4 by elimination method we get
Multiply `a+b =4`by 2 we get,
`4 = 4b`
`4/4=b`
By substituting b = 1 in a + b = 4 we get
`a+1 =4`
`a = 4-1`
`a =3`
Then a = 3, b = 1
Hence, the correct choice is `(b).`
APPEARS IN
संबंधित प्रश्न
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate α4 + β4
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 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)`
Find the condition that the zeros of the polynomial f(x) = x3 + 3px2 + 3qx + r may be in A.P.
If the zeros of the polynomial f(x) = x3 − 12x2 + 39x + k are in A.P., find the value of k.
Find the zeroes of the quadratic polynomial f(x) = 4x2 - 4x - 3 and verify the relation between its zeroes and coefficients.
Find the quadratic polynomial, sum of whose zeroes is 0 and their product is -1. Hence, find the zeroes of the polynomial.
If `x =2/3` and x = -3 are the roots of the quadratic equation `ax^2+2ax+5x ` then find the value of a and b.
Find a cubic polynomial with the sum of its zeroes, sum of the products of its zeroes taken two at a time and the product of its zeroes as 5, -2 and -24 respectively.
By actual division, show that x2 – 3 is a factor of` 2x^4 + 3x^3 – 2x^2 – 9x – 12.`
What should be subtracted to the polynomial x2 − 16x + 30, so that 15 is the zero of the resulting polynomial?
The polynomial which when divided by −x2 + x − 1 gives a quotient x − 2 and remainder 3, is
If p(x) = axr + bx + c, then –`"b"/"a"` is equal to ______.
If 2 and `1/2` are the zeros of px2 + 5x + r, then ______.
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
Find the zeroes of the following polynomials by factorisation method and verify the relations between the zeroes and the coefficients of the polynomials:
`4x^2 + 5sqrt(2)x - 3`
If one of the zeroes of a quadratic polynomial of the form x2 + ax + b is the negative of the other, then it ______.
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`
Find a quadratic polynomial whose zeroes are 6 and – 3.
