00:01
In this problem, we have been given a quadratic equation in x and one of the zeros of the quadratic equation is given.
00:10
So the given quadratic equation is x square plus 3x plus k.
00:20
And 1 .0 is equal to 2.
00:27
1 of the 0.
00:27
So a quadratic equation will have 2 zeros.
00:30
So 1 0 is given as 2 and we have to find the value of k.
00:34
So, k is some constant.
00:35
Now, we know that a zero of a polynomial means a number which we, if we replace it in terms of x, we get the value of the equation, value of the quadratic equation as zero, quadratic equation or quadratic function as zero.
00:51
So this is a quadratic function in terms of x.
00:54
So instead of x, if you put 2, we should be getting 0.
00:59
That is why the number 2 is called a 0 of this function.
01:02
Now instead of x put so let me represent this as f of x since it is a function okay so instead of x put x is equal to two then what will happen f of x should be equal to zero that is the definition of a zero of a polynomial or zero of a function yeah so instead of x if you put two what will happen in the function you get two the square two whole square instead of x two square plus 3 into 2 plus k this value should be equal to 0 see so that means 2 square is 4 plus 3 into 6 plus k equals to 0 therefore final answer is k is equal to minus 10 so we have found the value of k is equal to minus 10 okay so in the problem they have asked to verify the verify also so to verify we just have to rewrite the equation, rewrite the polynomial given, quadratic polynomial given.
02:09
So the quadratic polynomial is going to be x square plus 3x minus 10 now because we have found the value of k, which is minus 10.
02:18
Now just find the two zeros of this polynomial.
02:21
If you want to find the two zeros of the polynomial, what you are going to do? i am going to use a method called splitting the middle term.
02:30
So i am going to split the middle term such that x square plus.
02:33
5x minus 2x minus 10 so what i did here is instead of 3x i have replaced it with 5x minus 2x okay so how did i get the number 5 and minus 2 because in the method of middle splitting middle term we have to select any two numbers such that their sum is equal to 3 their product is equal to 1 into minus 10 that is minus 10 so that sum should be equal to 3 and the product should be equal to minus 10 in this case.
03:06
So, the sum is 3 here.
03:08
5 plus minus 2 is 3...