Pls solve the following questions in the image:
Also solve this:
9. If the polynomials 2x³ + ax² + 3x - 5 and x³ + x² - 4x + a leave the same remainder when divided by x-2, find the value of a.
10. The polynomials ax³ + 3x² - 3 and 2x³3 -5x + a when divided by (x-4) leave the remainders R₁ and R₂ respectively. Find the values of a in each of the following cases, if
(i) R₁ = R₂
(ii) R₁ + R₂ = 0
(iii) 2R₁ - R₂ = 0.
11. If the polynomials ax³ + 3x² - 13 and 2x³-5x + a, when divided by (x - 2) leave the same remainder, find the value of a.
Attachments:
Answers
Answered by
3
Answer:
Step-by-step explanation:
Let the given polynomials be f(x) and g(x).
When f(x) and g(x) are divided by (x-2) they leave the same remainder.
I.e (x-2) is a factor of f(x) and g(x). It means 2 is the zero of f(x) and g(x)
So that,
f(2) = g(2)
2x³+ax²+3x-5 = x³+x²-4x+a
2(2)³+a(2)²+3(2)-5 = 2³+2²-4(2)+a
2(8)+a(4)+6-5 = 8+4-8+a
16+4a+1 = 4+a
17+4a = 4+a
4a-a = 4-17
3a = -13
a = -13/3.
Similar questions
Chemistry,
3 hours ago
Computer Science,
3 hours ago
Math,
5 hours ago
CBSE BOARD XII,
7 months ago
Math,
7 months ago
Math,
7 months ago