Date | November 2017 | Marks available | 5 | Reference code | 17N.2.hl.TZ0.7 |
Level | HL only | Paper | 2 | Time zone | TZ0 |
Command term | Find | Question number | 7 | Adapted from | N/A |
Question
In the quadratic equation 7x2−8x+p=0, (p∈Q), one root is three times the other root.
Find the value of p.
Markscheme
METHOD 1
let roots be α and 3α (M1)
sum of roots (4α)=87 M1
⇒α=27 A1
EITHER
product of roots (3α2)=p7 M1
p=21α2=21×449
OR
7(27)2−8(27)+p=0 M1
47−167+p=0
THEN
⇒p=127 (=1.71) A1
METHOD 2
x=8±√64−28p14 (M1)
8+√64−28p14=3(8−√64−28p14) M1A1
8+√64−28p=24−3√64−28p⇒√64−28p=4 (M1)
p=127 (=1.71) A1
[5 marks]
Examiners report
[N/A]