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Quadratic Equations with Both Roots Common

For two quadr...

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For two quadratic equations to have both roots common, the ratio of the corresponding coefficients must be equal.

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Q. For two quadratic equations to have both roots common, the ratio of the corresponding coefficients must be equal.

Q. Say true or false.

A quadratic equation with integral coefficients must have integral roots.

Q. Assertion :Let

a, b, c

be real such that

a x^{2} + b x + c = 0

x^{2} + x + 1 = 0

have a common root.

a = b = c

Reason: Two quadratic equations with real coefficients cannot have only one imaginary root common.

Q. If the discriminants of two quadratic equations are equal and the equations have a common root 1, then the other roots (1) are either equal or their sum is 2 (2) have to be always equal (3) are either equal or their sum is 1 (4) have their sum equal to 1

Q. For a quadratic equation to have no real roots, its discriminant (𝑑) must satisfy:

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