Question

8. Find the zeroes of the quadratic polynomial 2x^2 - 7x -15 and verify the relationship between the zeroes and the coefficients.
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Answer 1

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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Answer 2

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Problem-}}}}}}$

Find the zeroes of the quadratic polynomial 2x^2 - 7x -15 and verify the relationship between the zeroes and the coefficients.

$\huge{\fbox{\fbox{\bigstar{\mathfrak{\red{Answer}}}}}}$

Given :-

2x^2 - 7x -15=0

To find :-

verify the relationship between the zeroes and the coefficients.

Solution :-

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2x²-7x-15=0

splitting the terms,

=> 2x²-10x +3x -15=0

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

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

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=> 2x+3=0

=> 2x=-3

=> x= (-3/2)

=> x-5=0

=> x=5

Hence,zeros polynomial are 5 and (-3/2)

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Relations(1)

sum of zeros= -(coefficient of x)/(coefficient of x²)

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putting values,

=>(-3/2)+5=-(-7)/2

=>(-3+10)/2=(7)/2

(7/2)=(7/2)

Hence,verified.

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Relation(2)

Product of zeros = (constant term)/(coefficient of x²)

=>(-3/2)×5=(-15/2)

(-15/2)=(-15/2)

Hence,verified

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