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5t² + 12t + 7. Find the zeroes of the polynomial, and verify the relation between the coefficients and the zeroes of the polynomial

Solution:

Given, the polynomial is 5t² + 12t + 7

We have to find the relation between the coefficients and zeros of the polynomial

Let 5t² + 12t + 7 = 0

On factoring,

= 5t² + 5t + 7t + 7

= 5t(t + 1) + 7(t + 1)

= (5t + 7)(t + 1)

Now, 5t + 7 = 0

5t = -7

t = -7/5

Also, t + 1 = 0

t = -1

Therefore,the zeros of the polynomial are -7/5 and -1.

We know that, if 𝛼 and ꞵ are the zeroes of a polynomial ax² + bx + c, then

Sum of the roots is 𝛼 + ꞵ = -coefficient of x/coefficient of x² = -b/a

Product of the roots is 𝛼ꞵ = constant term/coefficient of x² = c/a

From the given polynomial,

coefficient of t = 12

Coefficient of t² = 5

Constant term = 7

Sum of the roots:

LHS: 𝛼 + ꞵ

= -7/5 - 1

= (-7-5)/5

= -12/5

RHS: -coefficient of t/coefficient of t²

= -12/5

LHS = RHS

Product of the roots

LHS: 𝛼ꞵ

= (-7/5)(-1)

= 7/5

RHS: constant term/coefficient of t²

= 7/5

LHS = RHS

✦ Try This: Find the zeroes of the polynomial 7t² + 3t + 8, and verify the relation between the coefficients and the zeroes of the polynomial

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 2

NCERT Exemplar Class 10 Maths Exercise 2.3 Problem 3

5t² + 12t + 7. Find the zeroes of the polynomial, and verify the relation between the coefficients and the zeroes of the polynomial

Summary:

The zeroes of the polynomial 5t² + 12t + 7 are -7/5 and -1. The relation between the coefficients and zeros of the polynomial are. Sum of the roots = -b/a = -12/5, Product of the roots = c/a = 7/5

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