Advertisements
Advertisements
Question
Can the quadratic polynomial x2 + kx + k have equal zeroes for some odd integer k > 1?
Solution
A Quadratic Equation will have equal roots if it satisfies the condition:
b2 – 4ac = 0
Given equation is x2 + kx + k = 0
a = 1, b = k, x = k
Substituting in the equation we get,
k2 – 4(1)(k) = 0
k2 – 4k = 0
k(k – 4) = 0
k = 0, k = 4
But in the question, it is given that k is greater than 1.
Hence the value of k is 4 if the equation has common roots.
Hence if the value of k = 4, then the equation (x2 + kx + k) will have equal roots.
APPEARS IN
RELATED QUESTIONS
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`p(x) = x^2 + 2sqrt2x + 6`
Find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients
`g(x)=a(x^2+1)-x(a^2+1)`
If α and β are the zeros of the quadratic polynomial f(x) = ax2 + bx + c, then evaluate `beta/(aalpha+b)+alpha/(abeta+b)`
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 f(x) = `x^4– 5x + 6" is divided by g(x) "= 2 – x2`
On dividing `3x^3 + x^2 + 2x + 5` is divided by a polynomial g(x), the quotient and remainder are (3x – 5) and (9x + 10) respectively. Find g(x).
If \[\sqrt{5}\ \text{and} - \sqrt{5}\] are two zeroes of the polynomial x3 + 3x2 − 5x − 15, then its third zero is
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
Given that `sqrt(2)` is a zero of the cubic polynomial `6x^3 + sqrt(2)x^2 - 10x - 4sqrt(2)`, find its other two zeroes.
Find the zeroes of the quadratic polynomial 4s2 – 4s + 1 and verify the relationship between the zeroes and the coefficients.
