Question

Heya friends



Find zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients

$2x^{2}+\dfrac{7x}{2}+\dfrac{3}{4}$

Please answer fast and no spam or copying from internet as I am new to class 10 .

Answer 1

HEY THERE!!

◀ Question:

Find zeroes of the following quadratic polynomials and verify the relationship between the zeroes and their coefficients.

$2x^{2}+\dfrac{7x}{2}+\dfrac{3}{4}$

◀Answer:

Zeroes are -3/2 and -1/4.

◀ Explanation:

Solving the Quadratic Equation:

✒2x²+7/2x + 3/4

 ✒x²+ 3x+x/2 + 3/4

✒ x(2x+3) + 1/4(2x+3)

◀ For f(x) = 0

✒ x(2x+3) + 1/4(2x+3)= 0

✒   (x+1/4)(2x+3) = 0

•°• x = -1/4 or -3/2

Now, So the Zeroes of f(x) are -1/4 and -3/2.

◀ Sum of Zeroes = (-1/4) + (-3/2) = -7/4 = -(Coefficient of x)/(coefficient of x²)

◀ Product of Zeroes = (-1/4)×(-3/2) = 3/8  (constant term)/coefficient of x²)

◀ Hence, It's Verified!◀

Answer 2

2x²+7/2x + 3/4

x²+ 3x+x/2 + 3/4

x(2x+3) + 1/4(2x+3)




x(2x+3) + 1/4(2x+3)= 0

(x+1/4)(2x+3) = 0

x = -1/4 or -3/2




Sum of Zeroes = (-1/4) + (-3/2) = -7/8 = -Coefficient of x/(coefficient of x^2


Product of Zeroes = (-1/4)×(-3/2) = 3/8 constant term/coefficient of x^2