Question

Q2. If a and B are the zeroes of
the polynomial 5x² – 8x – 4, write the value of a + B + aß.​

Answer 1

Step-by-step explanation:

If alpha and beta are the zeroes of the polynomial 3x2-5x+8, then what is the alpha^2+beta^2?

Which is the best cement for building your home?

If alpha and beta are the zeroes of the polynomial 3x2-5x+8, then what is the alpha^2+beta^2?

Sorry, I don’t like alpha and beta; I’ll use p and q instead- heck, they’re quicker to type for a start!

A: Our original quadratic expression is; 3x2−5x+8

Now, if p and q are the roots, then:

3(x−p)(x−q)=0

Multiplying out the terms, we have:

B: 3x2−3(p+q)x+3pq=0

But, A and B are the same equation, so:

−3(p+q)=−5→p+q=53

3pq=8→pq=83

Now, (p+q)2=p2+2pq+q2

→p2+q2=(p+q)2−2pq

We know the values of p + q (from 1.) and pq (from 2.), thus:

p2+q2=(53)2−283

=259−163

=259−489

=−239