J17
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Example<br />
Solve the equation 2x 2 + 7x = 2<br />
Solution<br />
Writing the equation in the general form ax 2 + bx + c = 0 we get<br />
2x 2 + 7x - 2 = 0<br />
Hence a= 2, b = 7, c = -2<br />
Substitute these values in<br />
b<br />
( b<br />
2 4ac)<br />
x<br />
2a<br />
7 47 (4<br />
2 2)<br />
7 ± 65<br />
=<br />
=<br />
2<br />
2<br />
4<br />
Hence x = 0.27 or x = -3.77 (2 d.p)<br />
Example<br />
Solve: 2x(x – 1) = (x+ 1) 2 – 5<br />
Solution<br />
First we re-arrange the terms in the equation as follows.<br />
2x(x – 1) = (x + 1) 2 – 5<br />
⇔ 2x 2 – 2x = x 2 + 2x + 1 – 5<br />
2x 2 – 2x – x 2 – 2x – 1 + 5 = 0<br />
x 2 – 4x + 4 = 0<br />
(x – 2)(x – 2) = 0<br />
x = 2<br />
In this example the quadratic equation has a repeated root<br />
Exercise<br />
Solve the following, giving answers to two decimal places where necessary:<br />
1. 2x 2 + 11x + 5 = 0 2. 3x 2 + 11x + 6 = 0<br />
3. 6x 2 + 7x + 2= 0 4. 3x 2 – 10x + 3 = 0<br />
5. 5x 2 – 7x + 2 = 0 6. 6x 2 – 11x + 3 = 0<br />
7. 2x 2 + 6x + 3 = 0 8. x 2 + 4x + 1 = 0<br />
9. 5x 2 – 5x + 1 = 0 10. x 2 – 7x + 2 = 0<br />
11 2x 2 + 5x – 1 = 0 12. 3x 2 + x – 3 = 0<br />
13. 3x 2 + 8x – 6 = 0 14. 3x 2 – 7x – 20 = 0<br />
15. 2x 2 – 7x – 15 = 0 16. x 2 – 3x – 2 = 0<br />
17. 2x 2 + 6x – 1 = 0 18. 6x 2 - 11x – 7 = 0<br />
19. 3x 2 + 25x + 8 = 0 20. 3y 2 – 2y – 5 = 0
Change language