We have to find the relation between the coefficients and zeros of the polynomial
Let 4x² + 5√2x - 3 = 0
On factoring,
= 4x² + 6√2x - √2x - 3
= 2√2x(√2x + 3) - (√2x + 3)
= (2√2x - 1)(√2x + 3)
Now, 2√2x - 1 = 0
2√2x = 1
x = 1/2√2
Also, √2x + 3 = 0
√2x = -3
x = -3/√2
Therefore,the zeros of the polynomial are 1/2√2 and -3/√2.
We know that, if and ꞵ are the zeroes of a polynomial ax² + bx + c, then
Sum of the roots is + ꞵ = -coefficient of x/coefficient of x² = -b/a
Product of the roots is ꞵ = constant term/coefficient of x² = c/a
From the given polynomial,
coefficient of x = 5√2
Coefficient of x² = 4
Constant term = -3
Sum of the roots:
LHS: + ꞵ
= 1/2√2 - 3/√2
= (1-6)/2√2
= -5/2√2
= -5√2/4
RHS: -coefficient of x/coefficient of x²
= -5√2/4
LHS = RHS
Product of the roots
LHS: ꞵ
= (-3/√2)(1/2√2)
= -3/4
RHS: constant term/coefficient of x²
= -3/4
LHS = RHS
Therefore, the zeroes of the polynomial are -3/√2 and 1/2√2. The relation between the coefficients and zeros of the polynomial are, Sum of the roots = -b/a = -5√2/4, Product of the roots = c/a = -¾.
✦ Try This: Find the zeroes of the polynomial 4x² + 3√2x - 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 6
4x² + 5√2x - 3. 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 4x² + 5√2x - 3 are -3/√2 and 1/2√2. The relation between the coefficients and zeros of the polynomial are, Sum of the roots = -b/a = -5√2/4, Product of the roots = c/a = -¾
☛ Related Questions:
v² + 4√3v - 15. Find the zeroes of the polynomial, and verify the relation between the coefficients . . . .
y² + (3√5/2)y - 5. Find the zeroes of the polynomial, and verify the relation between the coefficien . . . .
7y² - (11/3)y - (2/3). Find the zeroes of the polynomial , and verify the relation between the coeff . . . .
A redox equation can be balanced using the following stepwise procedure: (1) Divide the equation into two half-reactions. (2) Balance each half-reaction for mass and charge. (3) Equalize the number of electrons transferred in each half-reaction. (4) Add the half-reactions together.
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Verified answer
Answer:
Step-by-step explanation:
Solution:
Given, the polynomial is 4x² + 5√2x - 3.
We have to find the relation between the coefficients and zeros of the polynomial
Let 4x² + 5√2x - 3 = 0
On factoring,
= 4x² + 6√2x - √2x - 3
= 2√2x(√2x + 3) - (√2x + 3)
= (2√2x - 1)(√2x + 3)
Now, 2√2x - 1 = 0
2√2x = 1
x = 1/2√2
Also, √2x + 3 = 0
√2x = -3
x = -3/√2
Therefore,the zeros of the polynomial are 1/2√2 and -3/√2.
We know that, if and ꞵ are the zeroes of a polynomial ax² + bx + c, then
Sum of the roots is + ꞵ = -coefficient of x/coefficient of x² = -b/a
Product of the roots is ꞵ = constant term/coefficient of x² = c/a
From the given polynomial,
coefficient of x = 5√2
Coefficient of x² = 4
Constant term = -3
Sum of the roots:
LHS: + ꞵ
= 1/2√2 - 3/√2
= (1-6)/2√2
= -5/2√2
= -5√2/4
RHS: -coefficient of x/coefficient of x²
= -5√2/4
LHS = RHS
Product of the roots
LHS: ꞵ
= (-3/√2)(1/2√2)
= -3/4
RHS: constant term/coefficient of x²
= -3/4
LHS = RHS
Therefore, the zeroes of the polynomial are -3/√2 and 1/2√2. The relation between the coefficients and zeros of the polynomial are, Sum of the roots = -b/a = -5√2/4, Product of the roots = c/a = -¾.
✦ Try This: Find the zeroes of the polynomial 4x² + 3√2x - 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 6
4x² + 5√2x - 3. 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 4x² + 5√2x - 3 are -3/√2 and 1/2√2. The relation between the coefficients and zeros of the polynomial are, Sum of the roots = -b/a = -5√2/4, Product of the roots = c/a = -¾
☛ Related Questions:
v² + 4√3v - 15. Find the zeroes of the polynomial, and verify the relation between the coefficients . . . .
y² + (3√5/2)y - 5. Find the zeroes of the polynomial, and verify the relation between the coefficien . . . .
7y² - (11/3)y - (2/3). Find the zeroes of the polynomial , and verify the relation between the coeff . . . .
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Answer:
A redox equation can be balanced using the following stepwise procedure: (1) Divide the equation into two half-reactions. (2) Balance each half-reaction for mass and charge. (3) Equalize the number of electrons transferred in each half-reaction. (4) Add the half-reactions together.
Step-by-step explanation:
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