Page 121 - Algebra

x = 10
Present age of Julie = x + 14 = 10 + 14 = 24 years
Present age of the grandmother = 10x + 14 = 100 + 14 = 114 years
Ratio= 24 = 4 or4:19 114 19
𝑥2−3𝑥+4 𝑥+2 𝑥2−4 × 𝑥−4
= 𝑥2−4𝑥+𝑥−4 × 𝑥+2 (𝑥−2)(𝑥+2) 𝑥−4
= 𝑥(𝑥−4)+1(𝑥−4) × 𝑥+2 (𝑥−2)(𝑥+2) 𝑥−4
= (𝑥−4)(𝑥+1) × 𝑥+2 (𝑥−2)(𝑥+2) 𝑥−4
= 𝑥+1 𝑥−2
12. The roots of the equation are: x = b = – 6√3, a = 9, and c = 3
11.
−𝑏±√𝑏2−4𝑎𝑐 2𝑎
6√3±√(−6√3)2−4(9)(3) 2(9)
x=
x = 6√3±√108−108
2(9)
x = 6√3 = √3 2(9) 3
When b2 – 4ac = 0, the roots of the equation are equal.
13. A quadratic equation has real roots when b2 – 4ac = 0
So,
(-k)2 – 4(3)(12) = 0 k2 – 144 = 0
k2 = 144
k = 12, –12
14. As –5 is the root of the x2 + px – 10 = 0
(–5)2 + p (–5) –10 = 0 25 – 5p – 10 = 0
15 = 5p
p =3
Now, 2x2 + qx + 2 has equal roots, So, b2 – 4ac = 0
q2 = 4(2) (2)
q =4
Page 120 of 177
Algebra I & II