Question

find the zeroes of the polynomial x²-2x- 35​

Answer 1

Method :-1

⇒By Middle term Splitting

Given equation are

⇒x² - 2x - 35 = 0

⇒x² - 7x + 5x - 35 = 0

⇒x(x - 7) + 5(x - 7)= 0

⇒(x + 5)(x - 7)=0

⇒x+5 = 0   and  x - 7 =0

⇒x = -5 and x = 7

Method ; 2

⇒by Quadratic Formula

⇒x = {(-b±√(b² - 4ac)}/2a

Given Equation

⇒x² - 2x - 35 = 0

Compare with

⇒ax² + bx + c = 0

We get

⇒a = 1 , b= -2 and c = -35

Now put the value on formula

⇒x = {-(-2)±√((-2)²-4×1×-35)}/2

⇒x = {2±√(4+140)}/2

⇒x = { 2±√(144)}/2

⇒x = { 2 + 12 }/2  and x = {2 - 12}/2

⇒x = 14/2  and x = -10/2

⇒x = 7 and x = -5

Answer 2

$\huge {\bf{\orange{\mathfrak{Answer:-}}}}$

$\Large\underline{\underline{\sf{\color{cyan}{GIVEN:-}}}}$

A polynomial x²+2x-35

$\Large\underline{\underline{\sf{\color{cyan}{To Find:-}}}}$

zeroes of the polynomial

$\Large\underline{\underline{\sf{\color{cyan}{Solution:-}}}}$

we have to spilt the middle term in such a way that the product come 35 and sum become 2

x²+2x-35

=>x²+7x-5x-35

=>X(X+7)-5(X+7)

=>(X+7) (X-5)

Now zeroes will be

$\boxed{\therefore{\sf x={5} \: , \: -7.}}$