1. Factorise : i) 2x3 – 3x2 -17x + 30 ii) 3x3 –x2 - 3x + 1
2. Divide the polynomial x3 - 4x2 + 5x – 2 by x2 – 3x + 2
3. Divide the polynomial x4 – 6x3 - 26x2 + 138x – 35 by x2 – 4x + 1
4. Find area of an equilateral triangle , if perimeter is 60m.
5. The curved surface area of a cylinder is 4400cm2 and the circumference of its base
is 110cm. Find the height of the cylinder.
6. If the mean of the data 2 , x+1 , 9 , x-2 is 4 then find the value of x .
7. The mean of 100 observations is 50. If the observation 50 is replaced by 150, what
will be the resulting mean?
8. A card is drawn at random from a well shuffled deck of playing cards. Find the
probability that the card drawn is
i)A card of spade or an ace ii) a red king iii) neither a king nor a queen
iv) either a king or a queen.
9. A die is thrown once. Find the Probability of getting
a) a Prime number ; b) a number lying between 2 and 6 ; c) an odd number
d) a number > 6 e) multiple of 5 or 6 f) a multiple of 2 and 3
g) a number greater than 4 h) not getting 1 or 6 .
10. A bag contains 12 balls out of which X are white.
i) If one ball is drawn at random, what is the probability that it will be a white ball?
PLS answer all to be marked as brainliest !!!
Answers
Step-by-step explanation:
The remaining zeros are -5 and 7.
Step-by-step explanation:
The given polynomial is
P(x)=x^4-6x^3-26x^2+138x-35P(x)=x
4
−6x
3
−26x
2
+138x−35
It is given that 2+\sqrt{3}2+
3
and 2-\sqrt{3}2−
3
are two zeros. It means (x-2-\sqrt{3})(x−2−
3
) and (x-2+\sqrt{3})(x−2+
3
) are factors of the given polynomial.
(x-2-\sqrt{3})(x-2+\sqrt{3})=(x-2)^2-3=x^2-4x+4-3=x^2-4x+1(x−2−
3
)(x−2+
3
)=(x−2)
2
−3=x
2
−4x+4−3=x
2
−4x+1
Divide the given polynomial by (x^2-4x+1).
\frac{x^4-6x^3-26x^2+138x-35}{x^2-4x+1}=x^2-2x-35
x
2
−4x+1
x
4
−6x
3
−26x
2
+138x−35
=x
2
−2x−35
It means the remaining factor of P(x) is x^2-2x-35x
2
−2x−35 .
x^2-2x-35=0x
2
−2x−35=0
x^2-7x+5x-35=0x
2
−7x+5x−35=0
x(x-7)+5(x-7)=0x(x−7)+5(x−7)=0
(x+5)(x-7)=0(x+5)(x−7)=0
Equate each factor equal to 0.
x=-5,x=7x=−5,x=7
Therefore the remaining zeros are -5 and 7.