Question

Find the zeroes of a quadratic polynomial 6x²+29x+35 and verify the relationship between the zeroes and the coefficients​

Answer 1

$X \: is -14 \: \: and -15$

Factorizing the equation,

⇒6x²−29x+35=0

⇒6x²−14x−15x+35=0

⇒2x(3x−7)−5(3x−7)=0

⇒(2x−5)(3x−7)=0

⇒x= 2/5 , 3/7

Answer 2

$\large\mathbf\red{ANSWER \: :}$

6x²+29x+35=6x² + 14x + 15x + 35 = 0

= (6x² + 14x) + (15x + 35) = 0

= 2x (3x + 7) + 5 (3x + 7) = 0

= (2x + 5) (3x + 7) = 0

Thus, (2x + 5) = 0 or (3x + 7) = 0

So, x = -5/2 or x = -7/3

Let the zero of the given quadratic polynomial be -5/2 and -7/3.

$\longrightarrow$Sum of zeroes = -5/2 + -7/3

= -15 - 14 / 6

= -29 / 6

=-(Coefficient of x)/Coefficient of x²

$\longrightarrow$Product of zeroes = -5/2 × -7/3

= 35 / 6

=Constant term/Coefficient of x²

$\large\mathbf\pink{PLS \: MARK \: AS \: BRAINLIEST \: .}$