Quadratic equation 12

1.(a) Find the sum and the product of the roots of px^2+qx-12=0 in terms of p and q.
Sum of roots = -q/p
Product of roots = -12/p
1(b) The graph of y = px^2 + qx - 12 cuts the x-axis at two points A(-2,0) and B(3,0).Find the values of p and q.
-2 and 3 are the 2 roots of px^2 + qx - 12 = 0
Product of roots = -6 = -12/p => p = 2
Sum of roots = 1 = -q/p => q = -2
2(a)The graph of y = -x^2 + mx + n cuts the x-axis at two points P and Q(5,0),and cuts the y-axis at the point R(0,15).
(i)Find the value of n.
Sub R into equation => 15 = n
(ii) Hence, find the coordinates of P.
Let P be (a, 0)
Prodcuts of roots = -n = -15 = 5(a)
a = -3
P is (-3, 0)
(b)Find the value of m.
Sum of roots = m = -3 + 5 = 2
3. Consider the quadratic equation 10x^2 - (3k+2)x + k = 0.If the sum of its roots is greater than the product of its roots by 4/5.
(a) find the value of k.
Sum of roots = (3k + 2)/10
Product of roots = k /10
(3k + 2)/10 - k /10 = 4/5
3k + 2 - k = 8
2k = 6
k = 3
(b) Hence,solve the equation.
10x^2 - 11x + 3 = 0
(5x - 3)(2x - 1) = 0
x = 3/5 or x = 1/2

1.(a) Find the sum and the product of the roots of px^2+qx-12=0 in terms of p and q.

Sum of roots = -q/p

Product of roots = -12/p

1(b) The graph of y = px^2 + qx - 12 cuts the x-axis at two points A(-2,0) and B(3,0).Find the values of p and q.

-2 and 3 are the 2 roots of px^2 + qx - 12 = 0

Product of roots = -6 = -12/p => p = 2

Sum of roots = 1 = -q/p => q = -2

2(a)The graph of y = -x^2 + mx + n cuts the x-axis at two points P and Q(5,0),and cuts the y-axis at the point R(0,15).

(i)Find the value of n.

Sub R into equation => 15 = n

(ii) Hence, find the coordinates of P.

Let P be (a, 0)

Prodcuts of roots = -n = -15 = 5(a)

a = -3

P is (-3, 0)

(b)Find the value of m.

Sum of roots = m = -3 + 5 = 2

3. Consider the quadratic equation 10x^2 - (3k+2)x + k = 0.If the sum of its roots is greater than the product of its roots by 4/5.

(a) find the value of k.

Sum of roots = (3k + 2)/10

Product of roots = k /10

(3k + 2)/10 - k /10 = 4/5

3k + 2 - k = 8

2k = 6

k = 3

(b) Hence,solve the equation.

10x^2 - 11x + 3 = 0

(5x - 3)(2x - 1) = 0

x = 3/5 or x = 1/2