Question

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

1️⃣ x² + 2x –1= 0
2️⃣ x² – x – 2 = 0
3️⃣ x² – 2x + 1= 0
4️⃣ x² + x + 2 = 0​

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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1. find the equation that formed by increasing each root of 2x²-3x-1=0by 1

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2. find the equation that formed by squaring each root of the equation x²+3x-2=0

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Answer 2

Given :- if p = 1 and q = –2 are roots of a quadratic equation, then quadratic equation will be ……………*

1️⃣ x² + 2x –1= 0

2️⃣ x² – x – 2 = 0

3️⃣ x² – 2x + 1= 0

4️⃣ x² + x - 2 = 0

Answer :-

given roots of the equation are (1) and (-2)

so,

→ sum of roots = p + q = 1 + (-2) = (-1)

and,

→ product of roots = (p * q) = 1 * (-2) = (-2) .

now, we know that , a quadratic equation can be written as ,

• x² - (sum of roots)x + product of roots = 0

putting values we get,

→ x² - (-1)x + (-2) = 0

→ x² + x - 2 = 0 (Ans.) (option 4)

Learn more :-

*What is the degree of the polynomial of 5x²y + 8xy² +9?*

1️⃣ 9

2️⃣ 5

3️⃣ 8

4️⃣ 3

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