examday

tmua.me papers

tmua.me Extreme Set A Paper 1 · Q14

Paper 1Algebra

The real constants a,b,ca,b,c have the property that both

x2−2ax+b≥0andx2−2cx+a≥0x^2-2ax+b\ge0 \qquad\text{and}\qquad x^2-2cx+a\ge0

hold for every real number xx.

What is the greatest possible value of

a+2c−6b ?a+2c-6b\,?
A38\dfrac38
B12\dfrac12
C1916\dfrac{19}{16}
D54\dfrac54
EThere is no greatest value\text{There is no greatest value}
F78\dfrac78

Read the questions freely. Sign in to check your answer, see the worked solution and save your progress.

Sign in to check your answerPractise the whole paper →