# maths

posted by .

Given that the roots of 2x^2-4x+5 are alpha and beta,find the value of ...
(i)alpha^3beta^3
(ii)(alpha-beta)^2

• maths -

Using the sum and product of roots property, we know
a+b = - (-4/2) = 2 and ab = 5/2, where a and b are alpha and beta

we know that
(a+b)^3 = a^3 + b^3 + 3a^2b + 3ab^2
(a+b)^3 = a^3 + b^3 + 3ab(b+a)
2^3 = a^3 + b^3 + 3(5/2)(2)
8 = a^3 + b^3 + 15
a^3 + b^3 = -7

in the same way....
(a-b)^2 = a^2 - 2ab + b^2
= a^2 +b^2 - 2ab

but a^2 + b^2 = (a+b)^2 - 2ab

so
(a=b)^2 = (a+b)^2 - 2ab - 2ab
= 4 - 5/2 - 5/2
= -1

• silly typo - maths -

in the third last line I should have had

(a-b)^2 = (a+b)^2 - 2ab - 2ab

## Similar Questions

1. ### Math

Given that sin alpha=4/sqrt65, pi/2<alpha<pi, and cos beta=-3/sqrt13, tan beta>0, find the exact value of tan(alpha+beta)
2. ### maths

if alpha and beta are the zeros of the polynomial 2x^2-4x+5 then find the values of (i)alpha^2+beta^2 (ii)1/alpha^2+1/beta^2 (iii)(r)alpha/beta+(r)beta/alpha (iv)alpha^-1+beta^-1
3. ### physics

Two radar stations A and B, are separated by horizontal distance of (a=500 metres), they both track the position of a plane C by recording angles (alpha), and (beta) at 1 second intervals. time (sec) 9 10 11 the angle A(alpha) 54.80 …
4. ### trig

evaluate the following in exact form, where the angeles alpha and beta satisfy the conditions: sin alpha=4/5 for pi/2 < alpha < pi tan beta=7/24 for pie < beta < 3pi/2 answer choices A. sin(beta+alpha) B. tan(beta-alpha) …
5. ### Math ( Polynomial )

This time three questions - 1. If (x^2 - 1 ) is a factor of polynomial ax^4 + bx^3 + cx^2 + dx + e, show that a + c + e = b + d = 0. 2. Let R1 and R2 be the remainders when polynomials x^3 + 2x^2 - 5ax - 7 and x^ 3 + ax^2 - 12 x + …
6. ### Math ( Polynomial )

This time three questions - 1. If (x^2 - 1 ) is a factor of polynomial ax^4 + bx^3 + cx^2 + dx + e, show that a + c + e = b + d = 0. 2. Let R1 and R2 be the remainders when polynomials x^3 + 2x^2 - 5ax - 7 and x^ 3 + ax^2 - 12 x + …
7. ### Math

If alpha and beta are the zeros of the polynomial ax^2 + bx + c then evaluateA. (alpha)^2 / beta + (beta)^2 / alpha B. alpha^2 .beta + alpha.beta^2 C. 1/(alpha)^4 + 1/(beta)^4. Please work the complete solution.
8. ### maths

If alpha beta are the roots of a^2 +bx + c = 0. find the values of (beta/alpha^2)+ (alpha/beta^2)
9. ### maths

If alpha and beta are the zeros of the polynomial p(x)=x^2+x+1 then find the value of 1÷alpha+1÷beta 2)alpha^2+beta^2
10. ### Math

If alpha, beta are the zeroes of x2-2x+3, find a quadratic equation whose roots are (alpha-1)(beta+1), (beta-1)(beta+1)

More Similar Questions