Question

if the zeros of the quadratic polynomial
${x}^{2} + (a + 1)x + b$
are 2and- 3 then the value of a and b are

Answer 1

In general, If there is a Quadratic equation such as ax² + bx + c, Then the sum of zeroes = -b/a and Product of the zeroes = c/a,

Given that, the equation is x²  +  (a+1)x + b, and zeroes of this are 2 and -3,
Sum of the zeroes is 2 + (-3) = 2-3 = -1,But also
Sum of zeroes is - (a+1)/1, So equal them,

=> -(a+1) = -1,
=> a + 1 = 1,
=> a = 0,

Product of the zeroes = 2*-3 = -6, But also, 
The product of zeroes is b/1,[Here c = b],
=> Equal them,
=> b = -6,

Therefore the value of a is 0 and the value of b is -6,

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