multiple input elements in form - React

It's a simple form which updates the state object onChange and displays that state object when submitted. I was not able to get it to work when there are multiple input elements.

Can anyone tell me what's wrong in this code? onSubmit works when there's only one input element, but not when there are multiple!

class ReactForm extends React.Component {
  constructor(props) {
    super(props);
    this.handleChange = this.handleChange.bind(this);
    this.validate = this.validate.bind(this);

    this.state = {
      name: "",
      email: ""
    };
  }

  handleChange(event) {
    event.preventDefault();
    const name = event.target.name;
    const value = event.target.value;
    this.setState({
      [name]: value
    });
  }

  validate(event) {
    event.preventDefault();
    console.log(this.state);
  }

  render() {
    return (
      <div>
        <form onSubmit={this.validate}>
          <div>
            <input
              type="text"
              name="name"
              value={this.state.name}
              onChange={this.handleChange}
            />
            <input
              type="email"
              name="email"
              value={this.state.email}
              onChange={this.handleChange}
            />
          </div>
        </form>
      </div>
    );
  }
}

ReactDOM.render(
  <ReactForm />,

  document.getElementById("root")
);