Question

find zeros of polynomial P(x) = 6x square - 19 X + 15 verify the relationship between zeros and coefficients

Answer 1

$\bold{\boxed{HEY!!!}}$

Here is your answer :-

P( x ) = 6x² - 19x + 15

6x² - 19x + 15 = 0

6x² - 10x - 9x + 15 = 0

2x ( 3x - 5 ) - 3 ( 3x - 5 ) = 0


$(2x - 3)(3x - 5) = 0 \\ \\ 2x - 3 = 0 \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: 3x - 5 = 0 \\ \\ x = \frac{3}{2} \: \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: x = \frac{5}{3}$




$\bold{\boxed{THANKS...}}$

Answer 2

P ( x ) = 6X² - 19X + 15

=> 6X² - 10X - 9X + 15

=> 2X ( 3X - 5 ) - 3 ( 3X - 5 )

=> ( 3X - 5 ) ( 2X - 3 ) = 0

=> ( 3X - 5 ) = 0 or ( 2X - 3 ) = 0

=> X = 5/3 or X = 3/2

So,

5/3 and 3/2 are two zeroes of the given quadratic polynomial.

• Relationship between the zeroes and coefficient.

Sum of zeroes = 5/3 + 3/2 = 10 + 9 / 6 = 19/6 = - ( Coefficient of X ) / Coefficient of X².

And

Product of zeroes = 5/3 × 3/2 = 15/6 = Constant term / Coefficient of X².