Question

Find a quadratic polynomial with the given numbers 4 and 1 as the sum and product of zeroes respectively.​

Answer 1

Answer:

x²-4x+1

Step-by-step explanation:

sum of the zeroes (a+B)=4

product of the zeroes=aB=1

let the quadratic polynomial be

ax²+bx+c

k[x²-(a+B)x+aB],

where K is constant and K is not equal to o then,

K[x²-(4)x+(1)]

If k=1 ,the quadratic polynomial with be

x²-4x+1

Answer 2

Answer:

= x² -4x + 1

Step-by-step explanation:

Let the polynomial be

p(x) = ax² + bx + c

Sum of zeroes = 4

-b/a = 4

assuming a = 1

-b/1 = 4

b = -4

Product of zeroes = 1

c/a = 1

assuming a = 1

c/1 = 1

c = 1

Now, a = 1, b = -4, c = 1

Hence required quadratic polynomial = ax² + bx + c

= x² +(-4x) + 1

= x² -4x + 1