Question

find the relationship between zeros and coefficients 2x^2+7x+6=0​

Answer 1

Answer:

-b+- √b2 -4ac/ 4a

roots are -2 & -3/2

Answer 2

Given :-

Quadratic Equation is 2x² -7x - 15 = 0

To Find :-

Zeros of The polynomial and verify their relation ships with the zeros.. ?

Solution :-

→ 2x² -7x - 15 = 0

Splitting The Middle Term we get,

→ 2x² -10x +3x - 15 = 0

→ 2x(x - 5) + 3(x - 5) = 0

→ (2x + 3)(x - 5) = 0

Putting Both Equal to Zero now, we get,

→ 2x + 3 = 0

→ 2x = -3

→ x = (-3/2)

Or,

→ x - 5 = 0

→ x = 5

Hence, Zeros of The polynomial are 5 and (-3/2).

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Now, First Relation is :-

→ Sum of Zeros = - (coefficient of x) /(coefficient of x²)

Putting both values ,

→ (-3/2) + 5 = -(-7)/2

→ (-3+10) /2= (7)/2

→ (7/2) = (7/2) ✪✪ Hence Verified. ✪✪

Second Relation :-

→ Product Of Zeros = Constant Term / (coefficient of x²)

Putting both Values ,

→ (-3/2) * 5 = (-15) / (2)

→ (-15)/2 = (-15)/2 ✪✪ Hence Verified. ✪✪

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