Question

37.if a and b are roots of quadratic equation x^2-1 = 0 form an equation whose roots are 2a/b and 2b/a​

Answer 1

Step-by-step explanation:

Given:if a and b are roots of quadratic equation x²-1 = 0

To find : An equation whose roots are 2a/b and 2b/a

Solution:

Find the roots of equation:

${x}^{2} - 1 = 0 \\ \\ {x}^{2} = 1 \\ \\ x = \sqrt{1} \\ \\ x = ±1$

Thus,

$a = 1 \\ \\ and \: \\ \\ b = - 1$

Find value of 2a/b and 2b/a

$\frac{2a}{b} = \frac{2 \times 1}{ - 1} \\ \\ = - 2 \:...eq1 \\ \\ \frac{2b}{a} = \frac{2 \times ( - 1)}{1} \\ \\ = - 2...eq2$

Now,Quadratic equation having roots (2b/a) and (2a/b)

as both the zeroes are -2,thus both factors are (x+2)

So,

Equation is

$(x + 2)(x + 2) = 0 \\ \\ \bold{\green{ {x}^{2} + 4x + 4 = 0 }}$

Hope it helps you.

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Answer 2

Answer:

x²+4x+4=0 is your answer