Question

One of the roots of the quadratic equation x²-8x+5-0 is 7.3166. The root of the equation correct to 4 significant figures is:​

Answer 1

Given:

one of the roots of the quadratic equation $x^{2} -8x+5=0$ is 7.3166

To Find:

The other root of the equation correct to 4 decimals

Solution:

To find the roots of the equation we can use the formula i.e

For an equation, $ax^{2} +bx+c=0$ we can use

                                      $x=\frac{-b\pm\sqrt{b^{2}-4ac }}{2a}$

now using the equation given and putting the values in the formula to find the roots for that compare every coefficient of the equation with the given equation to find the values

$a$=1

$b$=-8

$c$=5

Therefore ( we will get two values for the x as it is a quadratic equation, one root is given so to find the answer take the other root)

$x=\frac{8\pm\sqrt{64-20} }{2} \\=\frac{8\pm\sqrt{44} }{2} \\=4\pm\sqrt{11} \\=4\pm3.3166\\=4+3.3166,4-3.3166\\=7.3166,0.6833$

Hence, the other root of the equation x²-8x+5=0 is 0.6833

Answer 2

The root of the equation correct to 4 significant figures is 7.317

Given : One of the roots of the quadratic equation x²- 8x + 5 = 0 is 7.3166.

To find : The root of the equation correct to 4 significant figures

Concept Used :

Rule for rounding off a number :

Discard all digits to the right of the nth place , if the discarded number is less than half a unit in the nth place , leave the nth digit unchanged ; if the discarded number is greater than half a unit in the nth place , add 1 to the nth digit .

If the discarded digit is exactly half an unit in nth digit leaving the nth digit unaltered if it is an even number but increase it by 1 if it is an odd number

Solution :

Step 1 of 2 :

Write down the given number

Here it is given that one of the roots of the quadratic equation x²- 8x + 5 = 0 is 7.3166.

Step 2 of 2 :

Round off correct to 4 significant figures

The significant figures are 7 , 3 , 1 , 6 , 6

Digit at 5th significant figure = 6

Now 6 > 5

So we add 1 with the digit at 4th significant place

Hence the required number = 7.317

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