`x^2+x+1` is a .......... polynomial.
`(A)` cubic
`(B)` quadratic
`(C)` zero
`(D)` none of these.

If a (A) x=0 (B) x=1 (C) x=2 (D) None of these.

If alpha,beta are the zeros of the polynomial f(x)=x^(2)+x+1, then (1)/(alpha)+(1)/(beta)=( a) 1 (b) -1( c) 0 (d) None of these

If alpha,beta are zeroes of the polynomial x^(2)-2x-15, then form a quadratic polynomial whose zeroes are (2 alpha) and (2 beta)

The number of solution of the equation,log(-2x)=2log(x+1) is: zero (b)1(c)2 (d) none of these

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^(2)-1, find a quadratic polynomial whose zeros are (2 alpha)/(beta) and (2 beta)/(alpha)

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^(2)-1, find a quadratic polynomial whose zeros are (2 alpha)/(beta) and (2 beta)/(alpha)

Are the following statements 'True' or 'False'? Justify your answer. (i) If the zeroes of a quadratic polynomial ax^(2) +bx +c are both positive, then a,b and c all have the same sign. (ii) If the graph of a polynomial intersects the X-axis at only one point, it cannot be a quadratic polynomial. (iii) If the graph of a polynomial intersects the X-axis at exactly two points, it need not ve a quadratic polynomial. (iv) If two of the zeroes of a cubic polynomial are zero, then it does not have linear and constant terms. (v) If all the zeroes of a cubic polynomial are negative, then all the coefficients and the constant term of the polynomial have the same sign. (vi) If all three zeroes of a cubic polynomial x^(3) +ax^(2) - bx +c are positive, then atleast one of a,b and c is non-negative. (vii) The only value of k for which the quadratic polynomial kx^(2) +x +k has equal zeroes is (1)/(2) .

Assertion(A): The sum and product of the zeroes of a quadratic polynomial are (-1)/4 and 1/4 respectively. Then the quadratic polynomial is 4x^(2)+x+1 Reason (R):The quadratic polynomial whose sum and product of zeroes are given is x^(2) -(Sum of zeroes) x+ product of zeroes.

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^(2)-3x-2, find a quadratic polynomial whose zeros are (1)/(2 alpha+beta) and (1)/(2 beta+alpha)

If alpha and beta are the zeros of the quadratic polynomial f(x)=x^(2)-3x-2, find a quadratic polynomial whose zeros are (1)/(2 alpha+beta) and (1)/(2 beta+alpha)