Question

| Find the zeroes of the polynomial x2 + 3x - 10 and verify the relation between zeros and their
co-efficients.​

Answer 1

f(x)= x2 + 3x -10

finding zeros of f(x)

0= x2 + 5x - 2x - 10

0= x(x +5)-2(x + 5)

0= (x + 5)(x - 2)

x= -5 , x= 2

sum of zeros = -b/a = -5+2= -3

product of zeros= c/a = -5×2 = -10

hence verified

Answer 2

Solution:

=> p(x) = x² + 3x - 10

∴ For any zero p(x) = 0

Now,

=> x² + 3x - 10 = 0

=> x² + 5x - 2x - 10 = 0

=> x(x + 5) -2(x + 5)

=> (x - 2) (x + 5)

=> x = 2 and -5

∴ Zero of the polynomial = 2 and -5.

Here, α = -5 and β = 2

Now, we know that,

$\sf{\implies sum\;of\;zeroes=-\dfrac{b}{a}=\alpha+\beta=-5 + 2=-3}$

$\sf{\implies product\;of\;zeroes=\dfrac{c}{a}=\alpha \beta=-5\times 2=-10}$

Hence, it is verified!!