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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(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
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