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Chapter 7: Q. 7.147 (page 885)

Solve:

3c2=10c-8

Short Answer

Expert verified

The solutions of the quadratic equations 3c2=10c-8are c=43,2

Step by step solution

01

Step 1. Given Information

An equation:

3c2=10c-8

02

Step 2. Write the quadratic equation in standard form.

3c2=10c-83c2-10c+8=0

03

Step 3. Factor the quadratic expression

Factorize the equation,

3c2-10c+8=0(3c-4)(c-2)=0

04

Step 4. Use the Zero-Product property

Use the Zero Product Property and set each factor to zero.

(3c-4)(c-2)=03c-4=0c=43c-2=0c=2

The value of c is c=43,2

05

Step 5. Check the answer

Check by substituting the values in the original equation,

When c=43,

3(43)2=10(43)-8163=403-816-403=8-8=-8

When c=2,

3(2)2=10(2)-812=20-812=12

Hence the equations hold true.

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