Question

Verify that 2 and -3 are zeroes of the polynomial

p(x)= x2+x-6​

Answer 1

p(x)=x2−5x+4

To show: 4 and 1 are zeroes of p(x)

Proof: p(4)=(4)2−5(4)+4

p(4)=16−20+4

p(4)=20−20=0

p(1)=12−5(1)+4

p(1)=1−5+4

p(1)=5−5

p(1)=0

∵p(4) & p(1) is equal to zero

∴4 & 1 are the zeroes of p(x)

For polynomial ax2+bx+c having roots α & β

Sum of the roots =α+β= -b/a

Product of the roots =αβ= c/a

Sum of zeroes of p(x)=4+1=5

using above formula,

Sum of zeroes =−(−5)/1=5

Product of zeroes of p(x)=4×1=4

Using above formula,

Product of zeroes =4/1 =4

Hence, verified.