Tamilnadu State Board New Syllabus Samacheer Kalvi 11th Maths Guide Pdf Chapter 2 Basic Algebra Ex 2.6 Text Book Back Questions and Answers, Notes.
Tamilnadu Samacheer Kalvi 11th Maths Solutions Chapter 2 Basic Algebra Ex 2.6
Question 1.
Find the zeros of the polynomial function f(x) = 4x2 – 25
Answer:
Given f(x) = 4x2 – 25
To find the zeors of f(x), put f(x) = 0
∴ 4x2 – 25 = 0
⇒ 4x2 = 25
⇒ x2 = \(\frac{25}{4}\)
⇒ x = ±\(\sqrt{\frac{25}{4}}\) = ±\(\frac{5}{2}\)
Hence the zeros of f(x) are \(-\frac{5}{2}, \frac{5}{2}\)
Question 2.
If x = – 2 is one root of x3 – x2 – 17x = 22, then find the other roots of equation.
Answer:
Let f(x) = x3 – x2 – 17x – 22 = 0 —– (1)
Given that x = – 2 is a root of f(x).
∴ x + 2 is a factor of f (x)
Using synthetic division
Comparing equation (1) with the equation ax2 + bx + c = 0 we have
a = 1, b = – 3 , c = – 11
Question 3.
Find the real roots of x4 = 16.
Answer:
x4 = 16
⇒ x4 – 16 = 0
(i.e.,) x4 – 42 = 0
⇒ (x2 + 4)(x2 – 4) = 0
x2 + 4 = 0 will have no real roots
so solving x2 – 4 = 0
x2 = 4
Question 4.
Solve (2x + 1)2 – (3x + 2)2 = 0
Answer:
The given equation is (2x + 1)2 (3x + 2)2 = 0
(2x + 1 + 3x + 2) [(2x + 1) – (3x + 2)] = 0
[a2 – b2 = (a + b) (a – b)]
(5x + 3) (2x + 1 – 3x – 2) = 0
(5x + 3)(- x – 1) = 0
– (5x + 3)(x + 1) = 0
5x + 3 = 0 or x + 1 = 0
x = – \(\frac{3}{5}\) or x = – 1
∴ Solution set is { – 1, \(\frac{3}{5}\)}