Question

It's my homework...and the one who solves this correctly will be my brainliest man...or women...
Solve question no. 4 ,5, 6...plz need the solution right now tomorrow I gotta show it to my teacher...also question no. 9,10,12...

Answer 1

Q.9) What real number should be subtracted from from the polynomial 3x³+10x² -14x+9. So, that (3x-2) divides it exactly?

A.9) Given that p(x)= 3x³ + 10x² - 14x + 9
And 3x - 2 must divide it exactly, thus 3x-2 is a factor of p(x)
⇒ x= 2/3

Putting x=2/3 in p(x), we get:
3(⅔)³+10(⅔)²-14(⅔)+9

 =3(8/27)+10(4/9)-28/3+9

= 8/9 + 40/9 - 84/9 + 81/9

= (8+40-84+81)/9

= 45/9

= 5

Your answer= 5

Q.10) If the polynomial x^4 +2x³ +8x² +12x+18 is divided by another polynomial x^2 +5, the remainder comes out to be px+q. find the values of p and q .

A.10) First of all, divide x⁴ + 2x³ + 8x² + 12x + 18 by x² + 5
You'll get quotient= x² + 2x + 3
And remainder= 2x+ 3

ATQ, Remainder was in the form px +q, so p=2 and q=3

{P.S- If you have any problem in division, ask a separate question and I'll help you}

Q.12) Obtain all other zeroes of the quadratic polynomial x^4 + 4x³ - 2x² -20x -15. If two of its zeroes are √5 and -√5

A.12) Given that two of its zeroes are √5 and -√5, so its factors will be (x- √5) and (x + √5)

Multiplying, 
(x- √5)( x+ √5) = x² - 5  {Note: a² - b²= (a+b)(a-b)}

Now divide the p(x)=  x^4 + 4x³ - 2x² -20x -15. You'll get a quotient. Middle term split the quotient and you'll obtain two of its zeroes.