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Important Questions: Quadratic Equations


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Important Questions: Quadratic Equations - Question 1

Which of the following is a quadratic equation?

Detailed Solution for Important Questions: Quadratic Equations - Question 1

The correct answer is d

A quadratic equation (from the Latin quadratus for "square") is any equation that can be rearranged in standard form as. where x represents an unknown, and a, b, and c represent known numbers, where a ≠ 0. If a = 0, then the equation is linear, not quadratic, as there is no. term.

Therefore, x3 - x2 = ( x -1)3 is a quadratic equation.

Important Questions: Quadratic Equations - Question 2

Which of the following is not a quadratic equation?

Detailed Solution for Important Questions: Quadratic Equations - Question 2

Important Questions: Quadratic Equations - Question 3

Which of the following equations has 2 as a root?

Detailed Solution for Important Questions: Quadratic Equations - Question 3

Important Questions: Quadratic Equations - Question 4

Which of the following are the roots of the quadratic equation, x2 - 9x + 20 = 0 by factorisation?

Detailed Solution for Important Questions: Quadratic Equations - Question 4

 ∴ x = 4 and 5 are the roots/solution of the given quadratic equation

Important Questions: Quadratic Equations - Question 5

Value(s) of k for which the quadratic equation 2x2 -kx + k = 0 has equal roots is

Important Questions: Quadratic Equations - Question 6

If p,q and r are rational numbers and p ≠ q ≠ r, then roots of the equation (p2 - q2)x2 - (q2 - r2)x + (r2 - p2) = 0 are

Detailed Solution for Important Questions: Quadratic Equations - Question 6

Putting x = - 1, we have
∴ x = - 1 is one root.
Only option (d) has one root - 1.

Important Questions: Quadratic Equations - Question 7

The two consecutive odd positive integers, sum of whose squares is 290 are

Important Questions: Quadratic Equations - Question 8

If α, β are roots of the equation x2 + 5x + 5 = 0, then equation whose roots are α + 1 and β + 1 is

Detailed Solution for Important Questions: Quadratic Equations - Question 8

Important Questions: Quadratic Equations - Question 9

The quadratic equation with real co-efficients whose one root is 

Important Questions: Quadratic Equations - Question 10

Which of the following equations has two distinct real roots ?

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