Question

if one root of quadratics equations 2x2-5x+3a is 1 find the value of a​

Answer 1

Step-by-step explanation:

1 is one root of quadratic polynomial 2x² - 5x + 3a.

Hence, x - 1 is a factor of the polynomial.

x - 1 ) 2x² - 5x + 3a ( 2x - 3

2x² - 2x

- +

____________

- 3x + 3a

- 3x + 3

+ -

_____________

3a - 3

Remainder must be equal to 0 because x - 1 is a factor of the polynomial.

Now,

3a - 3 = 0

=> 3a = 3

=> a = 3/3

a = 1

Therefore, the value of a = 1

Answer 2

Answer:

-1/3

Step-by-step explanation:

From Remainder Theorem,

if 1 is a zero of polynomial p(x), p(1) = 0

∴ p(x) = 2x² - 5x + 3a

⇒ p(1) = 2(1)² - 1 + 3a = 0

⇒ 1 + 3a = 0

⇒ a = -1/3