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  • A quadratic equation with integral coefficient has integral roots. Justify your answer

A quadratic equation with integral coefficient has integral roots. Justify your answer

Answers (1)

False

Solution

Quadratic Equation – A quadratic equation in x is an equation that can be written in the standard form, ax^{2} + bx + c = 0   

Where a, b and c are real numbers with a \neq 0

Root: If ax^{2} + bx + c = 0                     …..(1)

Is a quadratic equation then the values of x which satisfy equation (1) are the roots of the equation.

 Let us take a quadratic equation with integral coefficient

 2x^{2}-3x-5=0

compare with ax^{2} + bx + c = 0 where a \neq 0

(a=2,b=-3,c=-5)

let us find the roots of the equation

 \\x=\frac{-b+\sqrt{b^{2}-4ac}}{2a}\\ x=\frac{3 \pm \sqrt{9-4(2)(-5)}}{2 \times 2}\\ x=\frac{3 \pm \sqrt{9+40}}{4}\\ x=\frac{3+\sqrt{49}}{4}\\ x=\frac{3+7}{4}=\frac{5}{7} \; \; \; \; \; \; \; \; x=\frac{3-7}{4}=-1

Here we found that 5/2 is not on integral

Hence the given statement is false

Posted by

infoexpert24

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