10)if one zero of the quadratic polynomial p(x)=3x²-8x+2k+1 is seven times the other zero's, then the value of k is *
1 point
3/2
-3/2
2/3
-2/3
11)x³-3x²+5x-3 is divided by x+2 then the remainder will be. *
1 point
32
-32
-33
33
Answers
10)
Solution :-
Comparing the given Quadratic polynomial p(x)=3x²-8x+2k+1 with ax² + bx + c = 0 we get,
→ a = 3
→ b = (-8)
→ c = (2k + 1)
Now, Let us Assume that, one zeros of given polynomial is m .
Than,
→ Other zeros = 7 * m = 7m .
So,
→ sum of Zeros = (-b/a)
→ (m + 7m) = -(-8)/3
→ 8m = 8/3
→ m = (1/3)
Therefore,
→ Zeros of Polynomial = (1/3) and (7/3) .
Now,
→ Product of zeros = c/a
→ (1/3) * (7/3) = (2k+1)/3
→ 7/9 = (2k+1)/3
→ 7/3 = 2k + 1
→ 7 = 3(2k + 1)
→ 7 = 6k + 3
→ 7 - 3 = 6k
→ 6k = 4
→ k = (4/6)
→ k = (2/3) (Ans.)
Hence, value of k will be (2/3) .
__________________________
11) Solution :-
we know that, if a polynomial p(x) is divided by (x - a) , than the remainder will be p(a) .
So,
→ x + 2 = 0
→ x = (-2)
Therefore,
→ p(x) = x³- 3x²+5x - 3
→ p(-2) = (-2)³ - 3(-2)² + 5(-2) - 3
→ p(-2) = (-8) -3*4 - 10 - 3
→ p(-2) = -8 - 12 - 13
→ p(-2) = (-33) (Ans.)
Hence, The remainder will be (-33).
Comparing the given Quadratic polynomial p(x)=3x²-8x+2k+1 with ax² + bx + c = 0 we get,
→ a = 3
→ b = (-8)
→ c = (2k + 1)
Now, Let us Assume that, one zeros of given polynomial is m .
Than,
→ Other zeros = 7 * m = 7m .
So,
→ sum of Zeros = (-b/a)
→ (m + 7m) = -(-8)/3
→ 8m = 8/3
→ m = (1/3)
Therefore,
→ Zeros of Polynomial = (1/3) and (7/3) .
Now,
→ Product of zeros = c/a
→ (1/3) * (7/3) = (2k+1)/3
→ 7/9 = (2k+1)/3
→ 7/3 = 2k + 1
→ 7 = 3(2k + 1)
→ 7 = 6k + 3
→ 7 - 3 = 6k
→ 6k = 4
→ k = (4/6)
→ k = (2/3) (Ans.)
Hence, value of k will be (2/3) .
__________________________
11) Solution :-
we know that, if a polynomial p(x) is divided by (x - a) , than the remainder will be p(a) .
So,
→ x + 2 = 0
→ x = (-2)
Therefore,
→ p(x) = x³- 3x²+5x - 3
→ p(-2) = (-2)³ - 3(-2)² + 5(-2) - 3
→ p(-2) = (-8) -3*4 - 10 - 3
→ p(-2) = -8 - 12 - 13
→ p(-2) = (-33) (Ans.)
Hence, The remainder will be (-33).