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Kinetic Friction

17. For the q...

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17. For the quadratic equation a * x ^ 2 + bx + c = 0, a, 1 and c are rational numbers and D = b ^ 2 - 4ac is a non-zero perfect square. The roots of the equation are

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Q. For the quadratic equation

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

c

are rational numbers and

D = b^{2} - 4 a c

is a non-zero perfect square. The roots of the equation are

Q. Assertion :If

a + b + c = 0

a, b, c

are rational, then roots of the equation

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

are rational. Reason: For quadratic equation given in Assertion, Discriminant is perfect square.

Q. For the quadratic equation

a x^{2} + b x + c = 0; a, b, c \in Q

if it's discriminant

D

is square of a non zero rational number, then it's roots will be

a, b, c

b^{2} - 4 a c

is perfect square then the roots of the equation

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

Q. Assertion :If

a + b + c = 0

a, b, c

are rational, then the roots of the equation

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

are rational . Reason: Discriminant of

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

is a perfect square .

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