(b) The zeroes of the quadratic polynomial x ^ 2 - x - 12 are i) - 3, - 4 ii) 4, -3 iii) 4,3 iv) -4,3
Answers
Step-by-step explanation:
Are algebraic expressions polynomials?
No, not all algebraic expressions are polynomials. But all polynomials are algebraic expressions. The difference is polynomials include only variables and coefficients with mathematical operations(+, -, ×) but algebraic expressions include irrational numbers in the powers as well.
Also, polynomials are continuous function (eg: x2 + 2x + 1) but algebraic expression may not be continuous sometimes (eg: 1/x2 – 1 is not continuous at 1).
Is 4 an algebraic expression?
No, 4 is not an algebraic expression because an expression should have at least one variable and one operation to be algebraic.
What are all the types of algebraic expressions?
There a
Answer:
Given:
We have been given a polynomial x² + x - 12.
To Find:
We need to find the zeroes of this polynomial.
Solution:
The given polynomial is x² + x - 12.
We can find the zeroes of this quadratic polynomial by the method of splitting the middle term.
We need to find two such numbers whose sum is 1 and product is -12.
Two such numbers are 4 and -3.
Substituting the values, we have
x² + 4x - 3x - 12 = 0
=> x(x + 4) - 3(x + 4) = 0
=> (x + 4) (x - 3) = 0
Either (x + 4) = 0 or (x - 3) = 0.
When (x + 4) = 0
=> x = -4
When (x - 3) = 0
=> x = 3
Hence, two zeroes of this polynomial are -4 and 3.
Step-by-step explanation: