Question

1 )If p and q are zeroes of f (x)=x2-5x+k, such that p-q=1,find the value of k.

2)If the zeroes of the quadratic polynomial x2+(a+1)x+b are 2 and -3,then find the value of a and b.

3) If one of the zeroes of the cubic polynomial x3+ax2+bx+c is -1 the find the product of the other two zeroes .

4)If a-b, a+b are zeroes of x3-6x2+8x ,then find the value of b.

5)Find a quadratic polynomial ,the sum and product of whose zeroes are root 2 and -3/2 respectively .Also find its zeroes.




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Answer 1

Answer:

(1) p is a zero of f(x)= x^2 -5x+k => f(p) = 0

=> p^2 - 5p +k = 0……..(1)

q is a zero of f(x)= x^2 -5x+k => f(q) = 0

=> q^2 - 5q +k = 0……..(2)

(1)-(2) gives p^2-q^2-5p+5q= 0

=>((p-q)(p+q-5)= 0

=> p+q-5=0 since it is given that p-q=1

=>p+q = 5

> p = 3 and q = 2

Substitute q=2 in (2). We get 4–10+k = 0=> k= 6

Answer 2

Answer:

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