Roots And Quadratic Equations
ADVERTISEMENT
1Roots and Quadratic Equations
2
ax
+ bx + c = 0
General Form of a Quadratic Equation is
If the roots of that quadratic equation are r
and r
, then x = r
or x = r
. We can write the
1
2
1
2
general form of a quadratic equation in the form of a product of two linear terms as
follows:
(x – r
)(x – r
) = 0
1
2
2
x
– (r
+ r
)x + r
r
= 0
1
2
1
2
2
By dividing the quadratic equation ax
+ bx + c = 0 by a, it can be rewritten as
2
x
+(b/a)x + c/a = 0
Comparing the coefficients in the two equations, we see that
1.
r
x r
= c/a
1
2
2.
– (r
+ r
) = b/a
or
r
+ r
= – b/a
1
2
1
2
In words, the product of the roots of a quadratic equation is c/a. The sum pf the
roots of a quadratic equation is –b/a
2
1.
Without solving, find the sum and product of the roots of x
+ 7x + 12 = 0.
2
2.
Without solving, find the sum and product of the roots of x
– 5x + 6 = 0.
2
3.
Without solving, find the sum and product of the roots of x
– x – 30 = 0.
2
4.
Without solving, find the sum and product of the roots of 8x
– 2x – 3 = 0.
2
5.
Without solving, find the sum and product of the roots of 6x
+ 13x + 5 = 0.
2
6.
Without solving, find the sum and product of the roots of 4x
= 23x – 15
7.
Find an equation whose roots are (– 4) and – 3.
8.
Find an equation whose roots are 6 and (– 5).
9.
Find an equation whose roots are 1/4 and (–2/3).
10.
Find an equation whose roots are (–2/5) and (–3/4).
11.
Find the equation whose roots are 2 + V3 and 2 – V3.
Hanlonmath
800.218.5482
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education