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Find a quadratic polynomial, the sum and product of whose zeroes are – 3 and 2, respectively.
Let the polynomial be $P(x) = ax^2 + bx + c$ Given Sum of Zeroes = -3 So, $-\frac{b}{a} = -3$ assuming a = 1 then, $-\frac{b}{1} = -3$ $\Rightarrow -b = -3$ $\Rightarrow b = 3$ Given Product of Zeroes = 2 So, $\frac{c}{a} = 2$ assuming a = 1 then, $\frac{c}{1} = 2$ $\Rightarrow c = 2$ Now a =Read more
Let the polynomial be
Given Sum of Zeroes = -3
So,
assuming a = 1 then,
Given Product of Zeroes = 2
So,
assuming a = 1 then,
Now a = 1, b = 3 and c = 2
Hence the required quadratic polynomial =
=
=
See lessFind the zeroes of the polynomial x² – 3 and verify the relationship between the zeroes and the coefficients.
Recall the identity a² – b² =(a – b)(a + b). Using it,we can write: x²-3=(x-√3)(x+√3) So the value of x²-3 is zero when x=√3 or x=-√3 Therefore, the zeroes of x²-3 are √3 and -√3 Sum of zeroes =√3-√3=-3/1=-(Coefficient of x)/(Coefficient of x²) Product of zeroes =(√3)(-√3)=(-3)/1 =(Constant tRead more