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Chapter 6: Q13. (page 297)

NUMBER THEORY Use a quadratic equation to find two real numbers whose sum is 5 and whose product is -14, or show that no such numbers exist.

Short Answer

Expert verified

The numbers are -2 and 7.

Step by step solution

01

Step-1 – Given

The sum = 5 and product = -14.

02

Step-2 – To determine

Use a quadratic equation to find two real numbers whose sum is 5 and whose product is -14, or show that no such numbers exist.

03

Step-3 – Calculation

Let the numbers are x and y.

So, the sum is x+y=5and product is xy=-14.

From x+y=5we get, y=5-x

Then we plug it in xy=-14and solve.

xy=−14x(5−x)=−145x−x2=−14x2−5x−14=0x2−7x+2x−14=0x(x−7)+2(x−7)=0(x−7)(x+2)=0x=7,−2

For ,y=5−x=5−7=−2

For , .y=5−x=5−(−2)=5+2=7

So, the numbers are -2 and 7.

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Most popular questions from this chapter

Solve each equation

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