MEDIUM
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Let α, β be the roots of x2+3x+5=0 , then the equation whose roots are 1 α and 1 β is

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Important Questions on Quadratic Equations

MEDIUM
Frame quadratic equations for the following roots.
-23,-14
MEDIUM

Form the quadratic equation from the roots 3 and -10.

HARD
The quadratic equation whose roots are the x and y intercepts of the line passing through 1, 1 and making a triangle of area A with the axes may be-
MEDIUM
Frame quadratic equations for the following roots.
2, -3
EASY

Two roots of quadratic equation are given; frame the equation.

1-35 and 1+35

HARD

Form the quadratic equation from the roots 12 and -12.

MEDIUM
A two digit number is four times the sum and three times the product of its digits. Find the number.
HARD
The value of a for which the sum of the squares of the roots of the equation x2-a-2x-a-1=0  assume the least value is
HARD
Sum of the roots of a quadratic equation is double their product. Find k if equation is x2-4kx+k+3=0.
EASY

If α, β are the zeroes of a polynomial x2-ax+b , such that α+β=6 and αβ=4, then find the value of a+b.

HARD
The sum of two roots of a quadratic equation is 5 and sum of their cubes is 35, find the equation.
EASY

Two roots of quadratic equation are given; frame the equation.

10 and -10

MEDIUM

Form the quadratic equation from the roots 0 and 4.

MEDIUM
Frame quadratic equations for the following roots.
12,-35
MEDIUM
The equation whose roots are reciprocal of the roots of the equation 3x2- 20x+17=0 is -
HARD

Form the quadratic equation from the roots 2-5 and 2+5.

HARD
If α β   but α 2 = 5 α - 3   and β 2 = 5 β - 3   then the equation whose roots are α β   and βα
EASY
When sum of roots =-7 and product of roots 5, then write the quadratic equation.
EASY

Two roots of quadratic equation are given; frame the equation.

0 and 7