Find the zeros of quadratic polynomial and verify the relationship between the zeros and coefficient
x²-17x-60
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SOLUTION.
Here, the equation is,
→ x² - 17x - 60 = 0
By splitting the middle term, we get,
→ x² - 20x + 3x - 60 = 0
→ x(x - 20) + 3(x - 20) = 0
→ (x + 3)(x - 20) = 0
By zero-product rule,
→ Either (x + 3) = 0 or (x - 20) = 0
→ x = -3, 20
★ So, the roots of the given equation are – -3 and 20.
VERIFICATION.
The standard form of a quadratic equation is –
→ ax² + bx + c = 0
Comparing the given equation with the standard form, we get,
→ a = 1
→ b = -17
→ c = -60
We know that,
→ Sum of roots = -b/a
→ Product of roots = c/aa
Here,
→ Sum of roots = -3 + 20 = 17
Also, using formula, we get,
Sum = -(-17)/1 = 17
Now,
→ Product of zeros = -3 × 20 = -60
Again, product using formula is -
= c/a
= -60/1
= -60
Hence, Verified.
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