Question

*जर p = 1 आणि q = –2 या किंमती वर्गसमीकरणाची मुळे असतील तर ते वर्गसमीकरण …………… आहे*​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

If p = 1 and q = –2 are roots of a quadratic equation, then quadratic equation will be

1. x² + 2x –1= 0

2. x² – x – 2 = 0

3. x² – 2x + 1= 0

4. x² + x - 2 = 0

CONCEPT TO BE IMPLEMENTED

If the roots of a quadratic equation are given then the quadratic equation is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes } = 0$

EVALUATION

Here it is given that p = 1 and q = –2 are roots of a quadratic equation

So

Sum of the zeroes = 1 - 2 = - 1

Product of the Zeroes = 1 × ( - 2 ) = - 2

Hence the required Quadratic equation is

$\sf{ {x}^{2} -(Sum \: of \: the \: zeroes )x + Product \: of \: the \: zeroes } = 0$

$\implies \sf{ {x}^{2} - ( - 1)x - 2 = 0}$

$\implies \sf{ {x}^{2} + x - 2 = 0}$

FINAL ANSWER

Hence the correct option is

4. x² + x - 2 = 0

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