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2 years ago

The quadratic equation x^2 + 3x + 50 = 0 has roots r and s. Find a quadratic equation whose roots are r^2 and s^2.

Mathematics

1 answer:

Stolb23 [73]2 years ago

7 0

Answer:

x^2 + 91x + 2500

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x^2 + 3x + 50

(x-r)(x-s)

-> x^2-(r+s)x+rs

rs = 50, r + s = -3

-> (rs)^2 = 2500

(r+s)^2 = 9

-> r^2 + 2rs + s^2 = 9

-> r^2 + 2(50) + s^2 = 9

-> r^2 + s^2 + 100 = 9

-> r^2 + s^2 = -91

(x-r^2)(x-s^2)

-> x^2-(r^2+s^2)x+(rs)^2

-> x^2 - (-91)x + 2500

x^2 + 91x + 2500

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skad [1K]

Answer:

Age of son = 6 years

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Step-by-step explanation:

GIVEN :-

A man is 5 times as old as his son. (In Present)
4 years ago , the man was 13 times as old as his son

TO FIND :-

The present ages of the man & his son.

SOLUTION :-

Let the present age of son be 'x'.

⇒ Present age of man = 5x

4 years ago ,

Age of son = (Present age of son) - 4 = x - 4

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The man was thirteen times as old as his son. So,

$=> 5x - 4 = 13(x - 4)$

Now , solve the equation.

Open the brackets in R.H.S.

$=> 5x - 4 = 13x - 52$

Take 5x to R.H.S. and -52 to L.H.S. Also , take care of their signs because they are getting displaced from L.H.S. to R.H.S. or vice-versa.

$=> 13x - 5x = 52 - 4$

$=> 8x = 48$

Divide both the sides by 8

$=> \frac{8x}{8} = \frac{48}{8}$

$=> x = 6$

CONCLUSION :-

Age of son = 6 years

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Read 2 more answers

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Answer: FALSE.

Step-by-step explanation:

Given the following equation provided in the exercise:

$x-13=x+1$

You need to solve for the variable "x".

In order to solve for "x" you can folllow the steps shown below:

1. You must apply the Addition property of equality and add 13 to both sides of the equation. Then:

$x-13+(13)=x+1+(13)\\\\x=x+14$

2. Finally you need to apply the Subtraction property of equality and subtract "x" from both sides of the equation. So you get:

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Which system of inequalities represents reglon Z? 6

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Step-by-step explanation:

step 1

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y=mx+b

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The solution of the inequality is the shaded area below the dashed line

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