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Squaring an Inequality

Let a, b be i...

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Let a, b be integers such that all the roots of the equation (x^2 + ax+ b)(x^2 + 17x + b) = 0 are negative integers, then the smallest possible value of a + b is

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Q. Assertion :If

a

b

are integers and the roots of

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

are rational then they must be integers. Reason: If the coefficient of

x^{2}

in a quadratic equation is unity then its roots must be integers.

Q. If the roots of the equation

x^{3} - a x^{2} + b x - c = 0

are three consecutive integers, then what is the smallest possible value of b?

Q. The quadratic equation,

x^{2} + a x + 12

can be factorised , where one of the roots

k

, is a negative integer. Then the possible value of

k

Q. If exactly two integers lie between the roots of the equation

x^{2} + a x - 1 = 0

, then possible integral value(s) of

a

a, b, c, d

be positive integers such that

a \geq b \geq c \geq d

. Prove that the equation

x^{4} + a x^{3} - b x^{2} + c x d = 0

has no integer solution.

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