Question

If x2 + 7x + 5k = 0, then the integral value of k for which the given equation does not have real roots can be

Answer 1

all from anthe mock test.Even i am confused with this.

Answer 2

Answer: $k=3, 4, 5, ...$

Step-by-step explanation: The given quadratic equation is

$x^{2} +7x+5k=0.$

Here, $a=1,~b=7,~c=5k.$

Since the equation does not have real roots, so we have the following inequality

$b^{2}-4ac<0\\ \Rightarrow 7^2-4\times 1\times 5k<0\\\Rightarrow 49-20k<0\\\Rightarrow 20k>49\\\Rightarrow k>\dfrac{49}{20}\\\Rightarrow k>2\dfrac{9}{20}.$

Since $k$ is an integer, so the values of k can be $3,~4,~5,...$