explain this question please I don't understand it
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Given : p(x) = x² + x - 12
To Find : zeroes of the quadratic polynomial
verify the relationship between the zeroes and the coefficients
Solution:
p(x) = x² + x - 12
x² + x - 12 = 0
=> x² + 4x - 3x - 12 = 0
=> x (x + 4) - 3(x + 4) = 0
=> (x - 3)(x + 4) = 0
Zeroes are 3 , - 4
Sum of zeroes = 3 - 4 = - 1
Product of zeroes = 3(-4) = - 12
ax² + bx + c = 0
product of zeroes = c/a
sum of zeroes = - b/a
comparing x² + x - 12 = 0 with ax² + bx + c = 0
a = 1 , b = 1 , c = - 12
product of zeroes = -12/1 = - 12
sum of zeroes = - 1/1 = - 1
relationship between the zeroes and the coefficients verified
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The nature of solutions if D = 0 is the roots are real and equal.
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