The graph of the quadratic trinomial `y=a x^2+b x+c` has its vertex at (4, -5) and two x-intercepts, one positive and one negative. Which of the following holds good? a. `a >0` b. `b<0` c. `c<0` d. `8a=b`

If the quadratic equation a x^2+b x+c=0(a >0) has sec^2thetaa n dcos e c^2theta as its roots, then which of the following must hold good? (a.) b+c=0 (b.) b^2-4a cgeq0 (c.) c ccgeq4a (d.) 4a+bgeq0

Which one of the following is correct for the graph of y=|x| ?

If a ,b in R ,a!=0 and the quadratic equation a x^2-b x+1=0 has imaginary roots, then (a+b+1) is a. positive b. negative c. zero d. Dependent on the sign of b

If one of the roots of the quadratic equation be x^2 - (1+b)x+6 = 0 be 2, then find the other root.

A quadratic trinomial P(x)=a x^2+b x+c is such that the equation P(x)=x has no real roots. Prove that in this case equation P(P(x))=x has no real roots either.

If the equation x^2=a x+b=0 has distinct real roots and x^2+a|x|+b=0 has only one real root, then which of the following is true? b=0, a >0 b. b=0, a 0, a >0

Let f(x)=a x^2+b x+c be a quadratic expression having its vertex at (3, -2) and value of f(0)=10 . Find f(x) .

The graph of (y-x) against (y+x) is shown below. Which one of the following shows the graph of y against x ?

The graph of (y-x) against (y+x) is shown. fig which one of the following shows the graph of y against x ?

If alphaa n dbeta are the roots of x^2+p x+q=0a n dalpha^4,beta^4 are the roots of x^2-r x+s=0 , then the equation x^2-4q x+2q^2-r=0 has always. A. one positive and one negative root B . two positive roots C . two negative roots D . cannot say anything