The graph of the quadratic trinomial `u=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 >0` b. `b<0` c. `<0` d. `8a=b`

Find p in R for which x^2-px+p+3=0 has one positive and one negative root.

Suppose a parabola y=ax^(2)+bx +c has two x intercepts, one positive and one negative, and its vertex is (2,-2). Then which of the following is true ? (A) ab > 0 (B) bc > 0 (C) ca > 0 (D) a + b + c > 0

If the quadratic equation ax^(2)+bx+c=0(a>0) has sec ^(2) thetaand cos ec^(2)theta as its roots,then which of the following must hold good? a.b+c=0 b.b^(2)-4ac>=0 c.>=4a d.4a+b>=0

The graph of a quadratic polynomial y= ax^2+ bx +c (a, b, c in R) with vertex on yaxis is as shownin the figure. Then which one of the following statement is CORRECT?(A) Product the roots the corresponding quadratic equation is positive.Aof of(B) Discriminant of the quadratic equation is negative.(C) Nothing can be the sum of the roots, whether positive, negative or zero.definite said about(D) Both roots of the quadratic equation are purely imaginary.

If a and b are positive integers, x and y are non-negative integers and a = bx + y, then which one of the following is correct ?

If the roots of the quadratic equation (a-b) x^(2) + (b - c) x + (c - a) =0 are equal , prove that b +c = 2a

If one of the zeroes of a quadratic polynomial of the form x^2 + ax + b is the negative of the other, then it

Using number line, how do you compare (a) two negative integers? (b) two positive integers? (c) one positive and one negative integer?

The roots of the quadratic equation (a+b-2c)x^(2)+(2a-b-c)x+(a-2b+c)=0 are