Question

The roots of the quadratic equation x²-4x-8=0 are 5.464,-1.464. The roots correct to 3 significant figures are 5.46 and -1.46 5.464 and -1.464 5.47 and -1.47 5.460 and -1.460 thank you so much miss ​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The roots of the quadratic equation x² - 4x - 8 = 0 are 5.464 , - 1.464

The roots correct to 3 significant figures are

5.46 and - 1.46

5.464 and - 1.464

5.47 and - 1.47

5.460 and - 1.460

CONCEPT TO BE IMPLEMENTED

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

EVALUATION

Here the given equation is x² - 4x - 8 = 0

The roots of the quadratic equation is 5.464 , - 1.464

We have to round off to 3 significant figures

4th significant figure of 5.464 = 4

4th significant figure of - 1.464 = 4

Since 4 is less than half of a unit

So we Discard all digits to the right of the 3 significant figures

Hence the roots correct to 3 significant figures are 5.46 and - 1.46 respectively

FINAL ANSWER

Hence the correct option is 5.46 and - 1.46

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