082-Engineering-Mathematics-Anthony-Croft-Robert-Davison-Martin-Hargreaves-James-Flint-Edisi-5-2017

so that
β=−13
Bycomparing coefficients ofx 2 we see that
2=α−4
Therefore,
α = 6
1.4 Polynomial equations 25
Hence,P(x) = (x −4)(x 2 +6x −13).Thequadraticequationx 2 +6x −13 = 0canbe
solved using the formula
x = −6 ± √ 36 −4(−13)
2
= −6 ± √ 88
2
= 1.690,−7.690
We conclude thatP(x) = 0 has roots atx = 4,x = 1.690 andx = −7.690.
EXERCISES1.4
1 Calculatethe rootsofthe following linearequations:
(a) 4x−12=0
(b) 5t+20=0
(c) t+10=2t
y
(d)
2 −1=3
(e) 0.5t−6=0
(f) 2x+3=5x−6
3x
(g)
2 −17=0
x
(h)
2 + x 3 = 1
(i) 2x−1= x 2 +2
(j) 2(y+1)=6
(k) 3(2y −1) =2(y +2)
3
(l)
2 (t+3)=2 (4t −1)
3
2 Solvethe followingquadraticequations by
factorization:
(a) t 2 −5t+6=0
(b) x 2 +x−12=0
(c) t 2 =10t −25
(d) x 2 +4x−21=0
(e) x 2 −9x+18=0
(f) x 2 =1
(g) y 2 −10y+9=0
(h) 2z 2 −z−1=0
(i) 2x 2 +3x−2=0
(j) 3t 2 +4t+1=0
(k) 4y 2 +12y+5=0
(l) 4r 2 −9r+2=0
(m)6d 2 −d−2=0
(n) 6x 2 −13x+2=0
3 Complete the square forthe followingquadratic
equations andhence findtheir roots:
(a) x 2 +2x−8=0
(b) x 2 −6x−5=0
(c) x 2 +4x−6=0
(d) x 2 −14x−10=0
(e) x 2 +5x−49=0
4 Solve the following quadraticequationsusingthe
quadraticformula:
(a) x 2 +x−1=0
(b) t 2 −3t−2=0