Advertisements
Advertisements
Question
If f(x) = ax2 + bx + c has no real zeros and a + b + c = 0, then
Options
c = 0
c > 0
c < 0
None of these
Solution
If f(x) = ax2 + bx + c has no real zeros and a +b + c < 0 then c< 0
Hence, the correct choice is `(c)`
APPEARS IN
RELATED QUESTIONS
Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
`t^2+1`
Give an example of polynomials f(x), g(x), q(x) and r(x) satisfying f(x) = g(x), q(x) + r(x), where degree r(x) = 0.
If 1 is a zero of the polynomial p(x) = ax2 − 3(a − 1) x − 1, then find the value of a.
If a quadratic polynomial f(x) is factorizable into linear distinct factors, then what is the total number of real and distinct zeros of f(x)?
If f(x) is a polynomial such that f(a) f(b) < 0, then what is the number of zeros lying between a and b?
If the product of two zeros of the polynomial f(x) = 2x3 + 6x2 − 4x + 9 is 3, then its third zero is
State whether the given algebraic expression are polynomial? Justify.
`2 - 5 sqrt x`
Obtain all the zeroes of the polynomial 2x4 − 5x3 − 11x2 + 20x + 12 when 2 and − 2 are two zeroes of the above polynomial.
Identify the following expression is polynomial. If not give reason:
`sqrt(5)x^2 + sqrt(3)x + sqrt(2)`
For the polynomial `((x^3 + 2x + 1))/5 - 7/2 x^2 - x^6`, write the coefficient of x6