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If the roots of the equation ax2 + bx + c = 0 are equal then c = ?
If roots of the equation ax2 + bx + c = 0 are equal
Then D = b2 - 4ac = 0
b2 = 4ac
Which of the following is a quadratic equation?
Which of the following is not a quadratic equation?
If x = 3 is a solution of the equation 3x2 + (k – 1)x + 9 = 0 then k = ?
If one root of the equation 2x2 + ax + 6 = 0 is 2 then a = ?
The sum of the roots of the equation x2 – 6x + 2 = 0 is
If the product of the roots of the equation x2 – 3x + k = 10 is - 2 then the value of k is
The ratio of the sum and product of the roots of the equation
7x2 - 12x + 18 = 0 is
If one root of the equation 3x2 - 10x + 3 = 0 is 1/3 then the other root is
If one root of 5x2 + 13x + k = 0 be the reciprocal of the other root then the value of k is
If the sum of the roots of the equation kx2 + 2x + 3k = 0 is equal to their product then the value of k is
The roots of a quadratic equation are 5 and - 2. Then, the equation is
If the sum of the roots of a quadratic equation is 6 and their product is 6, the equation is
If α and β are the roots of the equation 3x2 + 8x + 2 = 0 then = ?
The roots of the equation ax2 + bx + c = 0 will be reciprocal of each other if
If the equation 9x2 + 6kx + 4 = 0 has equal roots then k = ?
If the equation x2 + 2(k + 2)x + 9k = 0 has equal roots then k = ?
If the equation 4x2 - 3kx + 1 = 0 has equal roots then k = ?
The roots of ax2 + bx + c = 0, a 0 are real and unequal, if (b2 - 4ac) is
In the equation ax2 + bx + c = 0, it is given that D = (b2 - 4ac) > 0. Then, the roots of the equation are
The roots of the equation 2x2 - 6x + 7 = 0 are
The roots of the equation 2x2 - 6x + 3 = 0 are
If the roots of 5x2 - kx + 1 = 0 are real and distinct then
If the equation x2 + 5kx + 16 = 0 has no real roots then
If the equation x2 - kx + 1 = 0 has no real roots then
For what values of k, the equation kx2 - 6x - 2 = 0 has real roots?
The sum of a number and its reciprocal is . The number is
The perimeter of a rectangle is 82 m and its area is 400 m2. The breadth of the rectangle is
The length of a rectangular field exceeds its breadth by 8 m and the area of the field is 240 m2. The breadth of the field is
The roots of the quadratic equation 2x2 - x - 6 = 0 are
The sum of two natural numbers is 8 and their product is 15. Find the numbers.
Show that x = - 3 is a solution of x2 + 6x + 9 = 0.
Show that x = - 2 is a solution of 3x2 + 13x + 14 = 0.
If is a solution of the quadratic equation 3x2 + 2kx - 3 = 0, find the value of k.
Find the roots of the quadratic equation 2x2 - x - 6 = 0.
Find the solution of the quadratic equation 3√3x2 + 10x + √3 = 0
If the roots of the quadratic equation 2x2 + 8x + k = 0 are equal then find the value of k.
If the quadratic equation px2 –2√5px + 15 = 0 has two equal roots then find the value of p.
If 1 is a root of the equation ay2 + ay + 3 = 0 and y2 + y + b = 0 then find the value of ab.
If one zero of the polynomial x2 - 4x + 1 is (2 + √3 ), write the other zero.
If one root of the quadratic equation 3x2 - 10x + k = 0 is reciprocal of the other, find the value of k.
If the roots of the quadratic equation px(x – 2) + 6 = 0 are equal, find the value of p.
Find the values of k so that the quadratic equation x2 – 4kx + k = 0 has equal roots.
Find the values of k for which the quadratic equation 9x2 – 3kx + k = 0 has equal roots.
Solve:
Solve: 2x2 + ax – a2 = 0
Solve: 3x2 + 5√5x – 10 = 0
Solve: √3x2 + 10x – 8√3 = 0.
Solve: √3x2 – 2√2x – 2√3 = 0
Solve: 4√3x2 + 5x –2√3 = 0
Solve: 4x2 + 4bx – (a2 – b2) = 0.
Solve: x2 + 5x – (a2 + a – 6) = 0
x2 + 6x – (a2 + 2a – 8) = 0
x2 – 4ax + 4a2 – b2 = 0