The quadratic equation 2x2 – 3x + 5 = 0 has
The real roots of a quadratic equation ax2 + bx + c = 0 are given by
When b2 - 4ac=0 then we have the root as -b/2a.
When b2-4ac < 0,then the root is a complex root ,since we have a negative number ,for which real square root is not possible.
When b2 - 4ac > 0 then we have a square root of it and hence we have real roots. So the correct answer is b2 - 4ac > 0
The solutions of the quadratic equation are
The value of b2 - 4ac for equation 3x2 - 7x - 2 = 0 is
Which of the following is not a quadratic equation ?
For what value(s) of k will the equation kx2-5x+k = 0 have a repeated root?
A real number is said to be a root of ax2+bx+c = 0
-3 is a root of the quadratic equation 2x2 +px – 15 = 0. For what value of q, the equation p(x2 + x ) + q = 0 has equal roots?
The roots of x2 – 8x + 12 = 0, are
If 1/2 is a root of the equation x2+kx – (5/4) = 0, then the other root of the quadratic equation is
The sum of the ages of two friends is 20 years. Four years ago, the product of their ages in years was 48. Find their present ages
The nature of the roots of following quadratic equation
If the equation px2 – 6x – 2 = 0 has real roots then, ________
The positive value of k, for which both equations: x2 + kx + 64 = 0 and x2 – 8x + k = 0 have real roots is_______
If one root of a Quadratic equation is m +, then the other root is
In a quadratic equation with rational coefficients has an irrational root α + √β, then it has a conjugate root α - √β.
So if the root is m+ √n the other root will be m- √n
If the value of the Discriminant function of a quadratic equation is D = 27, then its roots are
Comment on the nature of the roots of the equation 7x - 3x2 - 2 = 0
The roots of the equation x2 – 3x – m (m + 3) = 0, where m is a constant, are
X2 - 3x - m(m+3) = 0
=> x2 + mx - (m+3)x- m(m+3) = 0
=> x(x+m) - (m+3)(x+m) = 0
=> (x+m) (x-m-3) = 0
x = - m and m+3
Roots are - m and m+3
If the equation 9x2 – 6x + c = 0 has equal roots then, the value of c is
If -3 is a root of both the Quadratic equations 2x2 + px – 15 = 0, and p(x2 + x) + q = 0, then the value of q if the equation containing it has equal roots is
-3 is root of both
2(9) -3p -15 = 0
p = 1
second equation has two equal roots so,
b2-4ac = 0
p2 = 4pq
p = 4q
q = 1/4
If a,b,c are real and b2-4ac >0 then roots of equation are
The quadratic equation whose roots are real and equal is:
Which of the following equations has two distinct real roots?
If the equation 2x2 + 2(c - 20) x + (c - 20) = 0 has equal roots then, the value of c is
Which of the following is a solution of the quadratic equation x2 - b2 = a (2x - a)