find the zeroes of the following quadratic polynomials and verify the relationship between the zeroes and the coefficients. x^2-9
Answers
Answer:
Zeros of eqⁿ x²-9 are 3 and -3
Step-by-step explanation:
∴ x²-9=0
∴ x²=9
∴ x = ±3
⇒ax²+bx+c=0
⇒x²-9=0
Comparing both eqⁿ
a=1, b=0, c= -9
⇒ Sum of zeros= -b/a
= 3+(-3)=-(0/1)
∴0=0 Hence verified.
⇒ Product of zeros= c/a
=3×(-3)= 9/1
= -9= -9 Hence verified.
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Answer:
x = ± 3
Note:
★ The possible values of the variable for which the polynomial becomes zero are called its zeros .
★ In order to find the zeros of the given polynomial , equate it to zero .
★ A quadratic polynomial can have atmost two zeros.
★ The general form of a quadratic polynomial is given by : ax² + bx + c .
★ If A and B are the zeros of the quadratic polynomial ax² + bx + c , then ;
• Sum of zeros , (A + B) = -b/a
• Product of zeros , (A•B) = c/a
Solution:
Here,
The given quadratic polynomial is ;
x² - 9
The given quadratic polynomial can be rewritten as ; x² + 0•x - 9
Clearly,
a = 1
b = 0
c = -9
Now,
Let's find the zeros of the given quadratic polynomial by equating it to zero .
Thus,
=> x² - 9 = 0
=> x² = 9
=> x = √9
=> x = ± 3
Now,
Sum of zeros = - 3 + 3 = 0
Also,
-b/a = -0/1 = 0
Clearly,
Sum of zeros = -b/a
Now,
Product of zeros = -3×3 = -9
Also,
c/a = -9/1 = -9
Clearly,
Product of zeros = c/a